It's funny how
// Speaking at a Westminster lunch yesterday, Miss Harman agreed that the next Doctor should be a Time Lady. //
Goes through the Daily Mail translator and comes out as
// Harriet Harman has demanded the BBC appoint a woman as the next Doctor Who. //
The Doctor does not have to be a male Gallifreyan. The character is fictional, so they writers can make the Doctor whatever they like. Saying that, making the programme an exploration of human gender roles is not what the programme is about, and would not work. If they got a good actress to play the role, but her sex was never mentioned, or an issue, then I would be OK with that.
It would be nice to get someone who can stay with the role for more than 2 seasons. We seem to have had a succession of short stay Doctors. It would be good to get someone to sign for 4 or 5 years.