Hmm. Honestly, I don't think it's a good idea. What about his relationships with companions? I mean, for example, what about Doctor and Rose? Can you imagine Nine's regeneration into someone like River or Missy?
I think it is a good idea to do this if not as a main doctor who then as a spinoff series. There already canon data that makes it possible for there to be a female doctor. But with change comes much dispute. On the same level as them announcing the next doctor was gonna be an old man. No fans will be 100% happy but if the writers stick to canon then they fans will eventually grow to love that character.
I think it could be a good idea (and now we have evidence that regenerations can change gender, if that wasn't known before). But I doubt they'd ever do it. It'd be too controversial and too many people would dislike it. People imagine the Doctor as male, some like to ship him with his Companions etc.
I, personally, find that I don't want a female Doctor. I've given this some thought and discussion among my friends.
I wouldn't mind if they did introduce a female Doctor, but I suppose I think of him as a guy. It would be interesting, certainly, to see how they handled it in the show with the Doctor's personal reaction and his (her) companions.
The fandom has been divided about this for awhile but I think YES. Don't get me wrong, I adore Capaldi! It's good to bring the classic Who back such as Capaldi before changing thing up. But in the future, BBC could do so much with a woman Doctor! I'm looking forward to it. They just gotta be very careful when casting ;) Also, can we just make her ginger?! He's waited long enough!