The thing you say about the Doctor being male eleven times--that's interesting, and I hadn't thought about that in this particular way. When I've thought about the possibilities for a female Doctor, I've guess I've kind of assimilated Time Lords to Trill (ST: DS9 was pretty formative for me as a sf fan/queer feminist person, can you tell?), in that I always assumed that gender would mean something different to them--meaningful for this particular body in this particular moment, but subject to change in phases. But even if so, it would certainly be jarring, even if the Doctor were OK with it in the end.

(This, of course, makes me want fic, written by people who could actually handle the complexities here. And it's yet another reason to be doubtful that the current writing staff of Doctor Who could actually handle aaaaaaany of the things that feminist fans might want.)