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Hey, Hillary. Australia’s first woman prime minister has some advice for you

June 15, 2015, 11:44 PM UTC

Julia Gillard’s three years and three days as Australia’s first female prime minister were tumultuous, to say the very least.

She took over as prime minister in what Americans might consider a coup and was ousted from her leadership role by members of her own party. In between, she delivered her so-called misogyny speech in Parliament in reaction to comments about sexism from opposition leader Tony Abbott. Gillard, who had been the target of sexist criticism of her hair, body image, and unmarried state during her tenure, told Abbott that if he wanted to see what misogyny looks like in modern Australia, he ought to look in the mirror. Viewers have watched her remarks on YouTube 2.5 million times.

And yet, when asked at Fortune’s Most Powerful Women summit in London on Monday to counsel Hillary Clinton on being the first woman to hold a prominent role, Gillard nearly side-stepped the question.

Clinton has been in politics a long time, Gillard said, so it’s doubtful that she needs any advice. But Gillard eventually provided this tip: “One thing I absolutely got wrong about being the first woman to do the job is that I made the assumption that the maximum reaction to being [the first female] prime minister would manifest itself in the first few months of doing the job; that would be its height.” Gillard says she figured that the more she did the job, “the more all of that would go away.”

As Gillard herself now knows, she was oh so wrong.

After assuming the job of prime minister in July 2010, her gender became a target for any critic of her government. When Gillard introduced a carbon tax in 2011, for instance, instead of just denying that climate change was real or human-made, as is typical, critics “degenerated into ‘ditch the bitch’ slogans,'” Gillard said on Monday.

Gillard said Clinton should address any sexism right away, so there are fewer chances it resurfaces later in her campaign.

Gillard also had advice for women everywhere: There’s an assumption that leadership and women don’t go together, she said. Until that ends, “we’ll be putting baggage on women who assume those roles,” she said. “This is the moment for us to be having deep conversations about how to change it so that daughters in the future [don’t have to face] questions other than those about values and competency and confidence.”