Notably, she became the first female Minister of foreign Affairs in Australia.
The Newspoll, published by The Australian newspaper, also showed Labor leader Bill Shorten was now preferred prime minister among voters.
She added she hasn't yet decided whether she will run for office in the country's next general election, set for 2019.
When some members of the group pointed out Bishop should be notified, another member, claimed to be Minister for Defence Industry Christopher Pyne, allegedly wrote: "I have".
The energy and environment portfolios, which used to have the same minister, have been severed under Mr Morrison's newly unveiled ministry.
"Despite our hearts tugging us to Julie we need to vote with our heads for Scott in round one".
"This is 100% incorrect", he said in his response.
Participants in the thread expressed some concern for the Foreign Minister, with one suggesting "Someone should tell Julie".
Turnbull tweeted that she was "an inspiring role model for women here and around the world".
However, on Tuesday last week, after Dutton was unsuccessful in taking leadership of the Australian Liberal Party from Turnbull when the first of several internal party votes saw the prime minister retain his title as chief, Dutton resigned from Home Affairs and took a seat on the backbench while Morrison took interim responsibility of DHA. None of the votes came from West Australians.
At times, her profile put her ahead of Turnbull in the popularity stakes.
But evidently, none of that was enough.
Turnbull had earlier given him Morrison his blessing to contest the leadership when he lost the majority support of his cabinet.
The museum said work on a wax figure depicting Mr Turnbull, intended for display...
"Without going over the entrails of last week".
"The era of the political assassin is over and thank God for that", Mr Abbott told Sydney Radio 2GB.
"I think as someone with local credentials and a strong track record of strong liberalism, I feel they are the types of candidates we want in any seat", Ms Forster said.
She has made no decision on whether she will stand at the next election.
Ms Bishop was knocked out in the first round of voting in what was a three-way battle for the leadership between her, Mr Morrison and Mr Dutton.
Former Prime Minister Malcolm Turnbull tweeted praise to Bishop saying she had been the nation's finest Foreign Minister and an inspiration to women globally.
"While Labor has at times been critical of the foreign policy directions under prime ministers Abbott and Turnbull, Ms Bishop's commitment to standing up for Australia both here and overseas has never been in question".