I have no problem with a female Doctor, just as I have no problem with a black Doctor, so long as there's someone who can play the part well, and from either angle I can think of four or five people who I'd be happy to see give it a try.
20-odd years ago I'd have felt differently, but that was probably more because black and female actors weren't getting roles that let them show themselves to be potential Doctors. Increasingly, they are.
But a definite no, no, no to Lara Pulver. At least, not until she's past 50. Helen Mirren now, yes. Helen Mirren in 1970, god no.