In the United Kingdom, Theresa May is Prime Minister and New Zealand has recently elected its third female prime minister, Jacinda Ardern.

But in Australia? Malcolm Turnbull's late 2017 cabinet reshuffle failed to increase the number of women in cabinet, while only one female name was added to the outer ministry. Meanwhile, only about 20 per cent of the Liberal partyroom are women, the lowest level since the early 1990s.

The situation is different on the Labor side – which introduced quotas in 1994 – where just under half of MPs are women. But it now seems a long time ago that Australia had a female prime minister.

When she lost the prime ministership in mid-2013, Julia Gillard said her experience would make it easier for other women to follow. But she also noted gender played some part in her downfall.

"It doesn't explain nothing; it explains some things, and it is for the nation to think in a sophisticated way about those shades of grey."

Virginia Haussegger, the director of the 50/50 by 2030 Foundation, said it was "difficult to even imagine a woman once again taking on the role of PM".

"The brief example we had in Julia Gillard was so fraught with a perverse fixation on her gender and perceived 'inadequacies' of women in leadership, that Australia still has a lot of growing up to do when it comes to getting our collective head around the inherent power of diversity."

Labor MP Anne Aly, who was a professor at Edith Cowan University before her election to Parliament in 2016, thought different standards are applied to women in leadership positions.

She noted that while ambition is seen as a positive attribute for men, for women it is a negative. Aly said characteristics that might be traditionally seen as more "female" – like empathy, negotiation and communication skills and bringing people together – tend to be overlooked when thinking about leadership.

It's easy to think of male prime ministerial contenders, be they more experienced MPs such as Scott Morrison, Peter Dutton, Christian Porter, Josh Frydenberg, Anthony Albanese or Chris Bowen. Or relative newcomers, such as Angus Taylor and Jim Chalmers.

But when Fairfax Media quizzed federal MPs and political observers about who they thought would be the next female PM, it was not similarly flooded with suggestions.

Elizabeth Broderick, a United Nations independent expert on gender equality and former Australian sex discrimination commissioner, said there was a "pipeline problem" with women in politics. She noted Parliament's long hours and travel requirements made it structurally difficult for women to have a family and forge a political career. Broderick added that while Gillard showed women and girls the top job was "no longer off limits," the gender-based abuse she experienced also meant "people saw how difficult it was".

"I wouldn't like to see another decade without a female prime minister," Broderick said.

So who might Australia's next female PM be?

"The way Malcolm Turnbull's governing, Julie Bishop's looking like she might be the next female prime minister," Aly said.

The deputy Liberal leader and Foreign Minister has a long and substantial parliamentary record, having been John Howard's education minister over 10 years ago. Immediate past president of Chief Executive Women, Diane Smith-Gander, noted Bishop looked "very comfortable" during her brief stints as acting prime minister last year. She is also an extremely hard worker, funny, and can more than hold her own in Question Time.

A recent Fairfax-Ipsos poll found Bishop as preferred Liberal leader among all voters polled, with 32 per cent, compared to 29 per cent for Malcolm Turnbull, 14 per cent for Tony Abbott, 5 per cent for Dutton and 4 per cent for Morrison.

But if there was a leadership spill before or after the next federal election, there are no guarantees Bishop would win. She faces an uphill battle to gain the support of the conservative wing of the party. And the Coalition has proven pretty resistant to women in leadership in recent years. Bishop has even previously spoken of the difficulties of being taken seriously in a male-dominated cabinet).

Some within Liberal circles caution that while she performs smoothly in the foreign affairs portfolio, the vast majority of the top job is domestic.

The deputy Labor leader since 2013, Plibersek is hugely popular with Labor ranks, particularly those on the left of the party. Bob Hawke has said she's "got everything it takes" and Gillard has described her as one of the most gifted communicators in the game.

An MP since 1998, Plibersek is valued for her sense of calm. She also has strong policy credentials as a former health and housing minister, with shadow roles in foreign affairs and now education.

When it comes to the leadership, she has adopted a wait-and-see approach: happy to be deputy, but also open to the top job if it became available. Even so, in the event of a spill if Labor lost the next election, Plibersek is not a certainty and would likely face competition from Albanese, Bowen and Tony Burke. As one Canberra watcher also noted, does she have that really ruthless streak required to go all the way to The Lodge?

The former finance minister is often cited as a potential prime minister: Haussegger nominated Wong as a contender for the role, while Smith-Gander praised her leadership during the recent same-sex marriage vote. The Labor Senate leader has a legendary ability to absorb information, is one of the best communicators in Parliament and is almost unflappable. The only problem is, Wong sits in the Senate.

While it would be possible for Wong to switch houses, the South Australian – who was also Australia's first Asian-born and openly gay cabinet member – has previously indicated she is not interested in running.

"There's too much sexism and homophobia and racism in our society for me to want to expose myself to that, and my family," Wong told BuzzFeed in 2015.

After Bishop, O'Dwyer is the second most senior Liberal woman in the lower house. She sits in cabinet as the Minister for Revenue and Financial Services and newly appointed Minister for Women. At 40, O'Dwyer spearheads a new breed of Gen X Liberals. Not only has she achieved a lot at a young age, she also has plenty of time on her side.

Labor's communications spokeswoman does not enjoy a huge public profile ... yet. She's a passionate local member, but also a policy gun, good at working with colleagues, a clear communicator and straight shooter.

The first-term Liberal MP comes to Parliament with an extensive legal and corporate career. While untested in a frontbench role, she's a smart, clear thinker, who is used to working under lots of pressure.

At 23, O'Neil became the youngest female mayor in Australian history. The Victorian Labor MP has since been a consultant at McKinsey & Company and a Fulbright scholar at Harvard. She has also co-authored a book on Australia's future with fellow Labor MP, Tim Watts. Despite the ferocious CV, O'Neil is refreshingly down to earth.

Fairfax Media contacted MPs on both sides of politics as well as leadership experts outside of politics and was struck by the lack of enthusiasm and ideas about existing female parliamentarians. On one level, this points to an overall bias about what makes a good leader. But it also suggests Australia's next female PM may not currently be in federal Parliament. Other contenders include:

The former NSW Labor premier not only has plenty of political experience, she is a tough cookie with bucketloads of charisma. Her recent unsuccessful attempt at the Bennelong byelection also proves she's willing to make the move to Canberra.

The current NSW Premier is focused on her state job and an election in 2019. But never say never. She's prodigiously hard working and her understated approach not only appeals to colleagues but voters, too.

As the head of the Australian Council of Trade Unions since 2010, Kearney has long been touted as a future federal MP. She's unlikely to make the PM's job any time soon, however. Last September, she surprised many in the labour movement by announcing a tilt at Victorian state politics.

Has ceiling-breaking form as the first female Lord Mayor of Sydney. And an impressive career that spans the law, business, government, philanthropy and the arts. As the partner of the current PM, she would also come to the job with no illusions.

Possesses a super CV for the job, with senior positions across a wide range of policy areas in the Victorian and NSW governments and a KPMG stint. She's been the head of the Business Council of Australia since 2011.