Georgia's mum, Jo Buckingham, has previously said even if her daughter is still alive next month, doctors say she will be too ill to go. The band, whom she met last year as part of Make a Wish, has however agreed to Skype Georgia in one of her final wishes.
The family was determined to still travel to Sydney for four days of fun, Jo Buckingham said today.
Switching airfares was expected to cost about $1000, but Air New Zealand had waived the fees, she said.
"It's very generous ... everybody who has given has just blown us away. There's the Givealittle and even in our own community, my hairdresser and two other [businesswomen] raised $3000 in three days."
Georgia had also been boosted by one of Five Seconds of Summer's band members following her on Twitter, Jo Buckingham said.
"She's very, very excited by that."