Rosie-Mai Backett passed away after she developed two infections following an operation.
Mother Amy Jarvis and father Shaun Backett, of St George's Avenue, were told 22 weeks into the pregnancy their daughter would be born with a heart defect.
Little Rosie-Mai died aged just nine months
They stayed at London's St Thomas' Hospital for two weeks after her birth.
She was at home for only two weeks after that before she needed to go back for surgery.
It would prove to be only a short-term solution and, after an MRI scan in September, it was decided she would need another heart operation in December at the Evelina Children's Hospital.
"We wanted her to see her first Christmas Day and she did. She waited for her nan and her aunty to say goodbye..." - father Shaun Backett
After the procedure she developed bronchiolitis and pneumonia, both of which affect the lungs. Rosie-Mai died on Boxing Day.
Mr Backett, 22, a phone salesman at O2 in Sittingbourne High Street, said: "On Christmas Eve she kept opening one of her eyes, looking to see if we were still there.
"By that time it was inevitable what was going to happen but we didn't want to believe it.
"We thought there was a faint hope. Every night we just thought if anybody could do it, she could.
"We wanted her to see her first Christmas Day and she did. She waited for her nan and her aunty to say goodbye."
After her heart rate kept fluctuating between low and high - before eventually stopping at 3.40pm on December 26.
Baby Rosie-Mai with her mother Amy Jarvis
Rosie-May had three siblings - Harry, nine, Daisy, seven and three-year-old Jack, who are Miss Jarvis's children.
Rosie-Mai's parents expressed their gratitude to Islanders who have rallied around. A fundraising page was set up on the Go Get Funding website for a memorial plaque at Emirates Stadium, as her father is an Arsenal fan.
A total of £770 has already been raised, surpassing the £495 needed. The extra money will go towards the funeral and any upkeep that is needed for Rosie-Mai's grave.
Miss Jarvis said: "I think it's amazing. I can't believe so many people care."
Mr Backett said: "It's hard to thank everybody and show appreciation, but we are extremely grateful."
Proud father Shaun Backett with little Rosie-Mai
The Queens Head pub will be hosting a charity pool and darts competition on Sunday to raise funds for Rosie-Mai's family with cash prizes for the winners.
It costs £5 to enter each event and there will be raffle prizes. Registration opens at 12.30pm, ready for a 1pm start.
Mr Backett is also planning to run the London Marathon in 2015 to raise money for the Evelina Children's Heart Organisation.
To sponsor him, visit www.virginmoneygiving.com/shaunbackett2014.
Anyone who knew Rosie-Mai is welcome to attend her funeral at Holy Trinity Church, Trinity Road, Sheerness, on Wednesday, January 15, at 11am.
The burial will be at Halfway Cemetery, Halfway Road, followed by a wake at the Co-op Sports and Social Club, St George's Avenue, Sheerness.
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