The airline admitted there had been "huge disruption".
The group of 242 people finally took off at 12:45am today after the flight to Doha had been grounded since 7:30am on Wednesday.
Passengers said they had to queue for up to five hours to check in last night because only one person was on the desk.
That followed the weary travellers being temporarily turfed out of their hotel rooms at the Edinburgh Marriott hotel after being put up there for the night while staff waited for authority from the airline to allow them to stay on.
They also complained of being given no information by Qatar Airways.
Australian Nick Cherry, who was returning home to the Gold Coast with his two daughters from a family funeral, said: "We are planning a class action involving 242 very irate passengers.
"At 4:30pm they turned up and announced we would be leaving at 8pm.
"What actually happened was we were taken to the airport at around 6pm and over the next five hours we crawled through check-in due to fact that Qatar Airways only have one trained ticketing agent in Edinburgh capable of sorting out the delay and re-ticketing.
"They didn’t even prioritise the elderly and families with children, who had to endure this five-hour line up.
"So we left exhausted at 12:45am and we didn’t get all our sectors re-ticketed, as they ran out of time, and we then spent another two hours in Doha this morning finishing the process."
Jonathan Couto, another passenger, wrote on Facebook: "We have now been sitting at the airport being told the departure will be at 7, then 8, then 1030, then 11, and at 1015 we are still nowhere near boarding.
"There is no food or drinks here - how is this acceptable? We should have departed almost 39 hours ago - how is this even possible for an airline like Qatar?"
Jan Spadavechia, who was travelling home to join her family in Adelaide, said: "I am exhausted and alone, full of anxiety because of this situation.
"We were put out of our rooms until the whole flight went off at Duncan from Qatar, then they let us book back in.
"The aircraft is still being fixed and everyone here is disgusted."
Fellow passenger Lesley Ballantyne, a teacher at Lesmahagow High School in South Lanarkshire, wrote on Facebook: "Qatar Airways ruined Christmas...new film coming out!
"We are all in it. 40 hours delayed... QATAR GIT ME TO AUSTRALIA!"
Edinburgh Airport said there had been a "technical issue" with the aircraft.
Qatar Airways responded to some of those who contacted them via Facebook to "express our sincere apologies for the huge disruption.
It said: "Rest assured our team has been working hard to resolve the issue and assist affected passengers."
A spokesperson told The Scotsman yesterday: "Qatar Airways regrets the delay of flight #QR 032 from Edinburgh to Doha and apologises for any inconvenience caused.
"Passengers were provided with food and hotel accommodation.
"All passengers will be assisted on an individual basis to ensure smooth onward connections to their final destinations.”
BACKGROUND: Edinburgh could get second flight to Qatar