City of Sydney Councillor Kerryn Phelps has thrown down a challenge to the Morrison Government, vowing to restore integrity and stability to Federal Parliament.

Professor Phelps, a prominent same-sex marriage campaigner and former AMA president, has confirmed she is running as an independent candidate in the Wentworth by-election.

She said the "revolving door of leadership" in Canberra over the past decade has weakened the standing of politicians and the major parties.

"I've had hundreds of people in Wentworth contact me in the past few weeks to express their anger and frustration over the sacking of Malcolm Turnbull," said Ms Phelps, who is looming as a wildcard in the October 20 vote.

"The new Prime Minister Scott Morrison either cannot or will not explain why Malcolm Turnbull has been replaced.

"What we need to see is some integrity and some stability returned to the Australian Federal Parliament."

The confirmation of Prof Phelps' candidacy comes just days after Liberal Party members selected Australia's former ambassador to Israel, Dave Sharma, as their candidate.

Mr Sharma was picked despite Prime Minister Scott Morrison making public his desire for a woman to be pre-selected for the blue ribbon seat.

Prof Phelps said she would push for action on climate change and energy policy, with "a fast-tracking to renewables".

She said she wanted to see a stronger economy "but we must have a heart", calling for more humane treatment of asylum seekers on Manus Island and Nauru.

Prof Phelps appeared in same-sex campaign 'Yes' advertisements in 2017. ( ABC News )

Prof Phelps played a key role in the same-sex marriage campaign last year and said her track record as a doctor, health communicator and advocate made for an appropriate skill set for Federal Parliament.

"The Yes campaign showed what happens when like-minded people come together in the interest of social justice," she said.

"The campaign for Wentworth will be a similar grassroots campaign by and for the people of Wentworth."

She expected the major parties to "throw big money and serious resources" at the electorate, but will be relying on donations from the community.

Wentworth — a federation electorate — has never been won by Labor. The Liberals hold it on a 17.7 per cent margin.

However, Prof Phelps' high profile could woo the eastern suburbs set, some of whom are annoyed at the Government for rolling their local member as prime minister.

Labor candidate Tim Murray, the Tamarama Surf Life Saving Club president, has already been campaigning while the Greens pick is Waverly deputy mayor Dominic Wy Kanak.