Lauren Heath, 20, was pushing her 11-month-old daughter Millie in a pram in Reading, Berkshire, when she was struck by a lorry on Wednesday 13 April.
Heath was pronounced dead at the scene, but thanks to her quick-thinking Millie suffered only a small cut.
Heath's friend Natasha Turner, from Edingburgh, set up a fundraising page with the hope of raising £500 for Millie, who turns one on Monday 18 April.
Within an hour of going live the GoFundMe page had surpassed its target and Turner told The Huffington Post UK she had been "overwhelmed" by the response.
"I just want to say thanks to everyone who donated," she said. "Even if it's only £1, every little bit helps and is going towards Lauren's send off and a future for Millie."
Following the accident, Millie was treated at the town's Royal Berkshire Hospital where she had stitches, and has since been allowed home.
Heath's family said in a statement: "Our daughter was such an amazing girl and the best mummy to Millie.
"She was her world and we are so proud that at the last time in her life she saved her baby girl."
Turner met Heath through a mum's group on social media.
"I spoke to Lauren quite regularly and got to know her quite well," she explained on the GoFundMe page.
"She was a doting mum to Millie and showed how much she loved her by sacrificing her self yesterday for Millie's safety."
Turner added that Heath had been "so excited" about Millie's upcoming birthday and "had already started planning things for her special day weeks ago".
Police are investigating the crash and have appealed for any witnesses to contact witnesses to contact the 24-hour Thames Valley Police enquiry centre on 101.
Senior investigating officer, Detective Sergeant Ashley Hannibal, from Thames Valley Police's Serious Collision Investigation Unit, said: "We are investigating the fatal collision and appealing for any witnesses who saw the collision or who saw the heavy goods vehicle travelling prior to the collision.
"Anyone with any information which could assist officers' enquiries should contact police."
Donations made to Turner's fundraising campaign will be split between covering the costs of Heath's funeral and invested in a trust fund for Millie.
People who have already donated have commented:
"It is amazing to see the true meaning of the word hero."
"What a brave young lady for saving her daughter's life."