What would they call her though? Dr. Whodina??
JK — this is a fantastic idea, and one that's time has come. Over at Slate, Laura Helmuth makes a compelling argument for the thousand-year-old time- and space-traveling alien oddball to live out loud in lady form:
The Doctor’s essential characteristics, the ones that show up in every reincarnation, are intelligence, courage, cleverness, adventurousness to the point of recklessness, and a sentimental affection for humans. The Doctor also has two hearts, but there’s no reason he has to have a penis.
We know it’s possible for Time Lords to switch genders when they are reincarnated. When the Doctor woke up in Smith’s body, he patted down his legs and face to get a feel for his new form, and he confirmed that he was a male by grabbing his … Adam’s apple. This would have been funnier if he hadn’t seemed so relieved.
Alyssa Rosenberg adds the excellent point:
If the Doctor is traveling around time and space in part in search of new experiences, it’s awfully incurious for him to keep reincarnating as a man, and as a white person. Wouldn’t he be curious, after all this time, to wonder what it’s like to occupy a woman’s body and to see what it’s like to live with a different set of gender roles (really, many different sets of gender roles)?
Sold! The next Dr. Who would definitely be a woman. Now, the question is... who should she be played by?