I don't watch Doctor Who myself (although one of my brothers is a big fan, I'm not sure what he thinks of a female Doctor) but I don't see the problem. All of the qualities of the character which differentiate them from humans are believable as part of the in-programme universe, but the Doctor being a woman isn't?
As its a Sci-Fi show, then the fact that a character could change sex is acceptable. However, the Doctor has been male for 50 odd years and there has never ever been any indication he could change gender - big clue in him being a Time Lord. You always knew the next incarnation of the doctor would be a man. If this was the 3rd or 4th doctor over say 5 years of the shows existence, then no-one would care, but they are re-writing 50 years of a show. I'm not particularly arsed what they do and it won't affect me as I'm no longer a fan of the show, since Tom Baker, the only series I've liked where the ones with David Tennant. However, I'll always see the doctor as a man, as that is how the character was written and has been played for 50 years.
I agree with Andy, if they want a strong female role model, then create one, don't steal a male role.