Hayley Brown has been devastated by the death of Oliver, her constant companion.
Police are appealing for witnesses to the hit-and-run, which happened on Crewe Road North at 10.20am on Tuesday.
The driver of the car which struck the King Charles spaniel is said to have slowed after the impact, then driven off.
Miss Brown is struggling to come to terms with the accident and says she does not know what to do without her puppy, who would have been two on October 7.
The 27-year-old had let Oliver out into the garden of a friend’s house on Crewe Loan, but he escaped through a neighbouring garden’s fence and ran out onto the road.
Miss Brown, who lives in Balerno, said: “I chased after him and I just heard a bang. I saw a car slow down. The guy looked at me, and I shouted at him to wait but as soon as I said that, he drove away.
“When I heard the bang, I knew it was my dog. It was louder than two cars crashing together. It must have broken all his bones instantly.
“He was on his back and his leg was twitching. His whole body was broken and he had blood coming out of his head. I had to pick him up because there were buses going past.
“I put him on the pavement and wrapped him up in my pashmina. He was dead, his tongue was hanging out.”
Miss Brown took Oliver to a vets, where he will be cremated, and a passer-by who witnessed the incident called the police.
She is planning on taking the ashes to all his favourite places – such as Arthur’s Seat, Portobello beach and Inverleith Park – one last time before scattering them.
Miss Brown, who is a web designer and runs her own modelling agency, was given Oliver as an early Christmas gift and said she had not been parted from him since.
“He was the most beautiful dog I’ve ever seen,” she said. “He just loved playing. He was very clever and had so much personality.
“He was cheeky. I don’t know what to do without him, my whole life revolved around my dog. I couldn’t sleep last night.”
She added: “There is nothing I can do or say to bring him back and that’s all that really means anything to me.
“It could easily have been a child that he hit. It was a child he hit – it was my child.”
The hit-and-run driver is described as an Asian man, around 40-years oldand wearing a turban. He was driving a marooncar which was travelling towards West Granton Road.
A police spokesman said: “The dog’s owner is utterly distraught at the loss of her pet and attempted to get the driver to stop after the collision. We are now carrying out local inquiries in the area to identify the car and anyone with information that can assist officers with their investigation is asked to contact police immediately.”