I still haven't finished working my way through all the seasons of the er, regenerated Doctor Who, but I do think the idea of a lady Doctor is really quite a fine idea, for several reasons. First, it would reinforce the character's alienness, something I think is a bit lacking, to inject the idea of a fluid concept of gender into the Time Lords' makeup.
Second, I've written about the fact that there's something nice about how the Doctor gives female companions (and faltering guys, too, in the case of Mickey) an opportunity to just embrace adventure without any larger motivation, just for the love of the trip. I'd like to see a woman, or to be more precise, a female character on the opposite end of the equation, be the native wayfarer, the lonely captain, the person who extends a hand and asks "Coming?" Some io9 commenters suggested that such a gender switch might end flirtations between the Doctor and companions, but I think it would be intriguing if a female Doctor was the seductive, compelling figure, as long as the show managed to build in some of the same emotional restraints, rather than making her an intergalactic cougar.
It's always been one of my great disappointments that the Pirates of the Caribbean movies ended with Elizabeth stuck on an island, raising a kid. She clearly had the mettle to captain a ship, to set her own course. We need more female swashbucklers, whatever crafts they choose to captain.