Tough question.
Gillard herself, in her farewell speech, displayed a salutary self-awareness when she said:
I do want to say the reaction to being the first female prime minister does not explain everything about my time in the prime ministership, nor does it explain nothing about my prime ministership.
There was sexist venom around Gillard’s prime ministership; the instances are known and uncontroversial.
But there was also a true disappointment in Gillard. In how her predecessor, a charismatic leader, was deposed without anyone explaining why. In how an engaged, activist education minister was transformed into a rigid, robotic prime minister. In how an atheist in a de facto relationship resisted marriage equality, rather than showing any leadership. In how her Misogyny Speech energised everyone in the world but politically engaged Australians, who knew the context was the whole sordid mess of the speakership of Peter Slipper.
Has it ruined the prime ministership for women? I don’t think so; it’s been two PMs since in the merry-go-round of Australian Federal politics, it’s already “Julia Who?” But then, I didn’t anticipate the outburst of sexism that hounded Gillard to begin with.
Could Julie Bishop do it? Probably not, loyal deputy too often, although she is one of the few members of the Abbott cabinet that commanded any respect at large. Could Penny Wong or Tanya Plibersek? Maybe. We were in a strange regressive place under Abbott, but a lot of people do want to move on. Which is why Turnbull was greeted as a saviour by everyone but the conservative true believers. (Remember that?)