You'd probably have to use a bus + tram to get there, but my doctor in North Carlton bulk bills, and I quite like her. Admittedly, I've never really had any major issues, so I'm not sure if she's A++ at the diagnostic stuff, but she's always done a decent job when she sees me. The medical centre she's at is also mostly devoted to treating women, if that matters to you.

Are you getting settled into you new place okay, absence of pizza delivery notwithstanding. (I have a pizza place just round the corner, so we never bother with getting it delivered. Just ring and pick it up)