I have had a few days to think about this and trying to be very careful how this comes out, but I am not happy with the idea of a female Doctor but (and this is the important bit) in the way that the BBC have decided to implement it.
For me there has to be a logical progression of the story, there has to be a reason for it and at this precise moment there is no reason. Oh, it could be argued that Moffat has been trying to pave the way for a female Doctor for the last season at least but the rules of the show (up until Missy) have clearly shown a male female divide between the Time Lords and Time Ladies (Any female Gallifreyan was always referred to as such indicating there was a gender divide between their sexes.)
We don’t really know how regeneration works, although there was a different effect for each of the classic show Doctors, it seems to have been standardised as the explosive effect in the modern Who. (It’s good I like it.) There seems to be a massive release of energy, and it completely rewrites the genetic structure of the regenerating individual, shrinking back into the new form quite nicely. When taken like this, if the regeneration is on such a minute scale there is no reason that the biology could not be altered in the process to switch between male and female.
I can believe that should a Time Lord regenerate naturally – gets old decides to regenerate then they could change gender, but it is not the way it has been portrayed in the show. The Doctor has had very few natural regenerations, his are generally caused by outside factors – really old age, poison, a long fall, smacking his head on the TARDIS console*
With this sudden and explosive regeneration, there should be no control over it. A total random regeneration, something that has been backed up by the Doctor’s reaction when checking himself out after the event. Therefore, it should be random. Totally. Male or female. 50/50 chance. Try flipping a coin 13 times, the chances of getting 13 heads in a row is very unlikely. The same is true with the regeneration, the Doctor should have been a woman before now. He hasn’t.
Until Missy, the Master regenerated from male to male.
Borusa, the Doctor’s old teacher appeared four times, each time he was male.
Romana regenerated once – controlled, with even a period of instability to try out bodies – unless she went through a lot of regenerations very quickly, each one female.
Leela married Andred, not once did they say, “Look, when I regenerate there might be a problem later!”
When the Sisterhood of Karn controlled the Doctor’s regeneration into the War Doctor there was no question of a woman.
Although I don’t really count it as canon, when the Doctor fought Morbius in the Brain of Morbius and we saw previous regenerations of either the Doctor or Morbius they were all male.
And when the Time Lords punished the Doctor at the end of the War Games forcefully, he was shown a number of faces to choose from (he rejected them all, so they chose John Pertwee), but not one of them were female.
It is easy to say that the Time Lords are meant to be so advanced that they are beyond gender, but all the evidence points to the opposite. They are meant to be a slowly decaying society, they have reached their peak and now crumbling.
Now, as Luiglin said, if there was a solid reason for the change – when the Doctor was granted a second set of regenerations after Matt Smith and he became female that would be acceptable, but only if she remained female throughout the next run of regenerations.
With all that being said, I’m interested to see where they take the show with a female lead. It will freshen it, make it different.
I’m not sure that I like the choice of actor, but then I’ve not seen her in anything so she deserves a chance, I just felt she did not seem otherworldly enough in the brief glance we have seen so far.
And, of course, there may be a very good reason for the gender swap, after all we have not seen the regeneration yet.
*come on, six to seven was an awful regeneration.