The girl and her brother have been identified as Katherine, 5, and Harry, aged 14 months - the only two children of 33-year-old mother Sok Ram.
The children were struck by the vehicle while crossing a street with their mother in Cabramatta, in Sydney's southwest, about 3.15pm on Wednesday.
Katherine was in her first year of kindergarten and had just been picked up after receiving an award, according to an online fundraiser on the family's behalf.
The children's lives were taken in a "split second", the man behind the fundraiser, Patrick Te, said.
"As they were crossing the road together, heading back to the car, an oncoming vehicle suddenly struck both Katherine and the pram where Harry was sitting," he said.
"A mother not only lost a child — she lost both of her children, her only two children."
The GoFundMe fundraiser had reached nearly $45,000 in donations by late on Thursday morning.
Paramedics treated the children at the scene and they were taken to hospital in a critical condition but died shortly after, police said.
Their mother was treated for minor injuries at the scene.
A 56-year-old man who was driving the car was uninjured and taken to hospital for mandatory testing.
NSW Police's crash investigation team is looking into how the incident happened.
Premier Chris Minns said it was a terrible event and everyone was heartbroken by the loss of the two young lives.
"This is one of those tragedies that hit the community incredibly hard," he said.
A number of witnesses tried to rescue the children but were unsuccessful, police said on Wednesday.
''The community involved here this afternoon was, I can only say, phenomenal,'' Acting Superintendent Timothy Calman said.
''We've had a number of motorists that actually stopped and collectively have moved the vehicle onto its side, tipped the car over in order to get one of the children from underneath the vehicle, and other bystanders have assisted with CPR.''
Mr Minns said he wasn't surprised to hear the good Samaritans had tried to save the children's lives with their "heroic efforts".