I think it'd definitely be cool, but then a lot of people are very used to the male doctor + female companion thing that's been going on for absolutely ever. Changing that up might lose them a lot of fans... In my experience, especially in regards to TV series and things like that, changing up "the formula" can cause a lot of unrest.
I'm sure he could change into a female, but it seems that Time Lords generally always stick to their same gender. The idea if kind of fun, but at the same time I don't really want to see it happen. That would be... weird some how.
That would be cool. Certainly it would make a great episode; I don't know how many people would like a full-time female Doctor, though. There would probably be a lot of criticism, unfortunately.
I think the Doctor has made passing mention to another Time Lord who regenerated from male to female, so it seems to be possible. The Doctor doesn't have as much control over his regenerations than other Time Lords, though. (For example, Romana went through a few different bodies before settling on one that she liked; the Doctor's regenerations seem to be completely random and not his choice at all.)