It would be nice if it were that easy. But Gillard was asked about this as recently as last October (well after she had resigned as PM).
As best I can figure her "logic," it goes something like this: she rejects marriage because she sees it as a patriarchal institution because women dress up in white to imitate virginity and are given away by men, etc. (never mind the fact that there is no law saying she has to do any of those things) but she made the CHOICE not to involve herself in that institution. And since she views it as anachronistic and patriarchal, she's actively using her beliefs to deny that choice to same-sex couples who might want to make a different CHOICE.
But it doesn't stop there. When Gillard was PM, she said, "I believe in the traditional definition of marriage." Huh?? So, it's patriarchal and anachronistic, but that tradition now needs to be protected from gay people?
Finally, in an interview with CNN from last November (again after she left office), she said, “I recognise that I had perhaps an eccentric view in some ways. I reasoned my way through to my own position through my own life experiences. And I didn’t want to impose it on anyone else.” Except that she did. Her public policy position on this was to deny same-sex couples the right to make that CHOICE for themselves because of her own beliefs that she rejected marriage but at the same time believed in the "traditional definition" of it..
So, she was letting her own convictions about marriage dictate what the public policy was rather than the popularism. BTW, an August 2013 poll by Fairfax Media and Nielsen Polling found that 65% favored making same-sex marriage legal.