But if the Doctor were to be written to kill innocents in cold blood, then that would not be canon, right? But it would be ok because it's a new creative direction?
Depends what you mean by "ok" really. Would it be artistically valid? Yes. Might it be entertaining? Yes. Would it be in keeping with the spirit of the programme? No.
Casting a female doctor is not against the spirit of the programme, which has always had a strong message of equality, using intelligence to solve problems and violence only ever as an absolute and regrettable last resort. There's nothing "core" to the concept of the show about the Doc's cock.
As for "canon" it's pretty meaningless for a show like Doctor Who, which has frequently contradicted itself over and over again. The story "The Ark in Space" from the mid-70s, has a plot where the Earth is abandoned for ten thousand years from the year 6087, but there are several other stories taking place on Earth during this period. There are also at least two different explanations for Atlantis.
The various comics, audio dramas and original novels around the show are all supposedly non-canon, except that the Doctor sometimes references them on screen. Does this mean all of them are canon? No, because they also contradict one another, and the show, all the time.
