Before you clicked on this article, you probably already had your mind made up regarding a female playing The Doctor simply because this is not a new idea. People have been floating the concept of casting an incarnation of The Doctor that isn't a white male for quite a while now with mixed response from both Whovians and casual watchers alike.
Imagining different actors and actresses in iconic roles has gone from something that was done only in "fan cast" style articles to a reality in some cases despite how vocal those are who do not appreciate these reimaginings. Some current examples of this are Paul Feig's "Ghostbusters" reboot, Michael B. Jordan as The Human Torch in the latest "Fantastic Four" movie, and all the clamor for Idris Elba to be the next James Bond.
Now, as a writer, I understand that there are lots of nuances that play into who a character is and that changing something fundamental about the character would involve adjusting those nuances to account for the change in perspective and experience - Doctor Who is different. This is not a "reimagining" of the character or the story. The Doctor's physical form changes to prevent his death - this is written into his (her?) character already! We aren't changing who the character is fundamentally, because the character is the same - just with a different physical form.
Earlier this year the fifth Doctor, Peter Davison, weighed in on the prospect of casting a female as The Doctor, saying it comes down to a "personal opinion" but that he does not think it would work. If you read my article (linked above) from January about his reasoning, you will see that none of the problems that he suggests casting a female Doctor would cause are game-changers. His suggestion that "if you're born on Gallifrey a man, you're probably a male Time Lord" operates outside of Doctor Who canon (Michelle Gomez portraying the now-female character The Master). The second point he raises is limited in scope to a Doctor whose personality doesn't evolve or change (though it does with every regeneration) and to a Companion that is of the opposite gender of The Doctor.
What do you think?