The conservative ruling Liberal-National coalition suffered a defeat Saturday in a Sydney constituency held by former Prime Minister Malcolm Turnbull before he was ousted in August.
"What we have done is tapped into a sentiment in the Australian people, to talk about the issues that are important to them, not the issues about survival for a particular political party", Phelps told supporters during her victory speech.
"I would like to say [to] any young people, any women, any aspiring independents out there, if you are thinking of running for Parliament or running for public office, yes, it can be tough, yes, the road can be hard, but it is so worthwhile that we have the right people stepping up to represent Australia".
At the heart of voter discontent in the traditional Liberal seat, which was held by Turnbull by an 18% margin, was widespread frustration about the leadership merry-go-round and constant infighting in Canberra.
On Saturday night, Phelps reflected on what she called a David and Goliath struggle, and thanked supporters, her wife Jackie and their children. "I would reject bad legislation".
It's the first time the sway has changed in 100 years. The opposition Labor Party holds 69 seats, while independents have six. The big issues of national importance.
With Phelps saying she has "no intention of bringing down the government", and other independent lawmakers also vowing to support Morrison's administration, it would seem unlikely that any no-confidence motion brought against the government between now and the election would succeed.
"I've certainly said that the government and all governments should go full term unless there are exceptional circumstances, and the next election is due in May next year, and that's time enough", Dr Phelps told ABC TV.
But this morning Mr Morrison said that while it was clear there was a significant swing against the Government, it was getting "tighter by the minute".
Instead, it would prefer Prime Minister Scott Morrison call a general election.
Mr Burke signalled Labor would be unlikely to put forward a no-confidence motion in the government, which would need 76 votes to succeed.
"I don't see how he can argue that and then not say we have to have an election". "That's what we want to see", he said.
Mr Morrison appeared to be bracing for a loss, saying he was prepared to govern without a majority. "Now we have a hung parliament".
In a stinging backlash from the electorate after the fourth toppling of an Australian leader by internal party vote in just eight years, a swing of more than 20 percent against the sitting Liberals propelled independent candidate Kerryn Phelps to a decisive victory.