As the pair neared their home, Daniel Jackson roared down a busy Edinburgh street high on a cocktail of drugs including heroin and Valium, colliding with a car.
The driver then careered through the suburb of Colinton, smashing the 1.5 ton Jeep into more cars, one of which struck and injured a pedestrian.
As Olivia, near right, and her mother were just yards away from the safety of their front door, Jackson, far right, swerved off the road, mounting a pavement and crushing the girl against her family's garden wall.
Olivia died at the scene, while Mrs Donachie, 33, later suffered the ordeal of having her left leg amputated.
The case, which yesterday saw Jackson admit a charge of culpable homicide at the High Court in Edinburgh, has triggered demands from politicians and campaigners for immediate action to tackle the problem of drug-driving.
They called for police to be given roadside testing kits to close a "loophole" which fails to discourage a significant minority of the population from getting behind the wheel of the car while under the influence of drugs.
The Scottish Campaign Against Irresponsible Driving went even further, urging politicians to introduce random driver testing for drugs and alcohol.
Surveys have shown as many as one in five youngsters take to the road while high on drugs. However, police have to rely on rudimentary tests such as asking motorists to walk in a straight line.
As a result, more than 1,700 drivers have escaped prosecution for driving under the influence because of insufficient or unreliable evidence.
Yesterday, the court heard Jackson was driving a Jeep Cherokee that was in such a state of disrepair it was effectively a death trap on the day he killed Olivia. He left a trail of damage following 20 minutes of mayhem during which he drove "like a maniac".
Dorothy Bain, QC, the advocate depute, told the court that an expert examined the vehicle after the fatal crash and "is of the opinion that the Jeep driven by the accused was the worst car he had ever examined in his ten years of working in this field".
"The Jeep was in poor condition and unsafe to drive and this should have been obvious to the driver. The Jeep simply had no footbrakes whatsoever," said Miss Bain.
Scientists later carried out tests on blood taken from Jackson and found his body was coursing with an astonishing cocktail of drugs, including heroin, the heroin substitute methadone and diazepam.
Drug addict Jackson told police that he had an almost daily intake of 40 of heroin, 70ml of methadone and four valium tablets.
Miss Bain said: "On the day of this incident he recalls taking two or three valium and also 60ml of methadone. He also claimed to have taken 20 to 30 valium the previous night, together with an injection of heroin.
"Despite this, he states that he felt totally okay to drive."
Jackson fled the scene after the fatal crash but later turned up at a psychiatric hospital in an effort to admit himself having slashed his wrists.
He told a doctor: "I have done something bad" and added: "I killed a little girl." Jackson said he might have taken both heroin and methadone that day and had run away.
While he was in a police cell, Jackson, a father of three of Grassmarket, Edinburgh, said: "I deserve life for what I have done - a life for a life." He added: "I deserve everything I get."
He told officers who interviewed him that on the day of Olivia's death, 30 May this year, he had been "posing" - just driving around.
The court heard that Jackson had already hit a car stopped at a red light in Lanark Road before causing another crash, in which a woman at a bus stop, Irene Muir, 60, was injured because of his driving.
Jackson drove on six streets in the city having consumed a quantity of controlled drugs, knowing brakes on the vehicle were defective and "with criminal disregard for the safety of other road users and in particular pedestrians".
As Miss Bain described the events that led up to the child's death, Jackson, who has previous convictions for robbery, assault and theft, sat in the dock with his head bowed.
On the day of the crash he had driven to Ormiston, in East Lothian, to collect David Ness before they went to visit a harm- reduction organisation in Edinburgh that provides support to addicts in the community.
Ness collected his prescription for methadone and Jackson was given 20 syringe-type needles.
Witnesses said the Jeep was on the wrong side of the road, accelerating and travelling at between 45 and 70mph when it entered Redford Drive, a largely residential street with a 30 mph speed limit.
Miss Bain said: "One witness describes the driver hunched over the wheel in an aggressive posture and turning to speak to the male passenger."
The Jeep was seen to skid or slide and then crash into a wall and bounce in the air.
Ness said that he told Jackson: "You better stop or you are going to hit that woman and bairn."
Miss Bain said Ness kept shouting at him to stop but Jackson kept "booting it on" before trying to slam on the brakes.
The noise of the Jeep hitting the wall was described as like "a bomb going off". Jackson and Ness emerged from the crashed vehicle bleeding from minor cuts.
Jackson pleaded guilty to killing Olivia and seriously injuring her mother outside their home at Redford Drive by driving at excessive speed and mounting a pavement and colliding with them.
The prosecutor said: "The Donachie family are a close, loving and supportive family." Mrs Donachie and her husband, Paul, 39, have three other children; Samuel, seven, Amelia, two, and Isabella, who was born two weeks before her eldest sister was killed.
Mrs Donachie worked as an intensive therapy nurse and her husband works with an investment firm, while Olivia went to a nursery attached to Bonaly Primary School.
"She has been described as a healthy, confident, outgoing child, who had lots of friends," said Miss Bain.
The defence counsel, Gordon Jackson, QC, said it was a "very anxious and extremely serious matter".
Lord Menzies deferred sentence on Jackson until 9 October at the High Court in Glasgow for the preparation of background and psychiatric reports. Jackson was remanded in custody.
Isobel Bridie, who chairs the Scottish Campaign Against Irresponsible Driving (SCID), said it was outrageous that police were not yet equipped with roadside drug-testing kits.
"A considerable percentage of people drive while impaired through drugs. This is the 21st century. You would expect police to have reliable, scientific roadside tests. This is a huge loophole and is fuelling the perception among drivers that it's OK to get behind the wheel after taking drugs."
She also called for random tests to clamp down on both drug and drink-driving.
Bill Aitken, justice spokesman for the Scottish Conservatives, said: "This is a classic illustration of what the Conservative group has been saying for the last two years.
"We have to clamp down on people driving while under the influence of drugs. There is general parliamentary agreement in this respect and once the test equipment is to hand, I would expect and demand its immediate introduction as a tool to combat this problem."
But he said random roadside tests for drugs or alcohol was "a step too far".
Nigel Griffiths, the MP for Edinburgh South, added: "This is a really serious issue. Police tell me this is one of these loopholes that's going to have to be addressed.
"With modern technology we have to improve on the walk-along-white-line test. This case shows that drug-driving is every bit as serious as drink-driving. As we have seen, the consequences couldn't be any more tragic.
"We need a breathalyser for drugs and, in the absence of that, police should have the power to take keys off drivers if there is any suspicion."
A Home Office spokeswoman said it was currently developing a specification for roadside drug screening devices and hoped to issue this to manufacturers later in the year.
THE SUBSTANCES IN HIS BLOOD
• HEROIN (DIAMORPHINE) Class-A drug with a street value of 30-50 a gram. The maximum penalty for possession is seven years in prison or an unlimited fine, or both. The penalty for dealing is life imprisonment, an unlimited fine, or both.
It is a sedative made from the opium poppy and is usually taken in tablet form or prepared for injection. It can also be smoked or snorted.
Users feel lethargic but experience severe cravings for the drug.
The vast majority of the drug comes from the so-called "Golden Crescent" region including Afghanistan, Iran and south-west Asia.
• VALIUM (DIAZEPAM) This a prescription-only tranquilliser - without a prescription it is classified as a Class-C drug.
The maximum penalty for possession is two years in prison or an unlimited fine, or both. Dealers face a maximum jail sentence of 14 years, an unlimited fine, or both.
Available without prescription on the internet. 30 10mg tablets cost about 20.
These drugs are used medically to treat anxiety, epilepsy and sleeplessness. Side-effects can include impaired co-ordination and depression.
They are normally swallowed in tablet or capsule form and have a calming and "slowing-down" effect, causing drowsiness.
• METHADONE (HEROIN SUBSTITUTE) A prescription-only synthetic drug with painkilling properties. Without a prescription it is a Class-A drug.
The effects are similar to heroin - euphoria and sedation - though it is less addictive, which is why the drug is widely used as a substitute for patients attempting to combat heroin addiction.
It is usually prescribed to addicts under the supervision of a pharmacist. However, heroin addicts have created a vast methadone black market by selling on their doses for as little as 2. It usually comes as a green liquid but can also be supplied as tablets, dispersable tablets or ampoules (for injection).
A driving licence is invalid if the holder is on a methadone treatment programme.