Christina Finn, 31, applied for a permanent residency visa five months ago after being married to her Scottish husband Chris for more than five years.
But she was left "heartbroken" after receiving a letter of refusal earlier this week, telling her she has until Tuesday to leave the country.
She had failed to provide documents which the Home Office required as evidence to support her application and it was therefore refused.
However, a friend helped her launch a fundraising page yesterday which explained her desperate circumstances in a bid to help fund a new application.
Each permanent visa application costs Â£3,000, and she will need to fork out Â£3,000 in lawyer fees to ensure there are no problems with the documents this time round.
The couple, who have just renovated their home in Trinity Crescent, have paid about Â£10,000 in visa applications down the years, meaning they are strapped for cash.
But within 24 hours of launching the fundraising page the Â£6,000 target was surpassed, with Â£6,200 raised as of 10am this morning.
Speaking today after reaching the fundraising target, Christina said: "We just want to thank everyone who has donated, we are just so overwhelmed and emotional with it all. It's just been incredible."
She added: "As we were going to bed (on Thursday night), all my friends and family in Australia were getting up and I think they all shared it and that helped as well.
"D-Day is Tuesday and it's the last chance to get the documents in order and our lawyer will work her hardest to make sure it's ready.
"We'd done it two times before and thought we'd be fine, but obviously not. A lot of people have come to her and said 'I wish we'd come to you from the start.'"
Christina was advised against appealing the decision to refuse her application because the process can take up to two years - and because there is a good chance she would lose.
Re-applying for the 'indefinite leave to remain' visa means she won't be able to attend her brother's wedding in Australia next month, as the Home Office must keep hold of her passport throughout the process. It would also be difficult for her to get back into the UK given her circumstances.
Christina met her musician husband Chris, 32, while working in a Royal Mile pub as he played there regularly in a band.
They married in February 2013 and she was granted a spouse visa, which was successfully renewed three years ago.
A Home Office spokesman said yesterday that all visa applications are considered on their individual merits and in line with immigration rules.