If she crashes a spaceship from the future, that would be no different than one of the male Doctors doing it. If she crashes a party in the 19th century, that would be the beginning of something interesting. I'm actually looking forward to stories taking place in the past, because the show may get an interesting change of perspective there.Will the Doctor be able to just take charge in historical situations or will it be more of a challenge? Is the new Doctor going to make more commentary on sexual politics or not? Even things like when the Doctor showed up at Bill's house with the roommates, does that play differently with a woman?
However, given the past Doctor's personalities, and how all her incarnations have handled being the elephant in the room so far—ignoring any social norms and dodging all questions—she still wouldn't need to change herself even the slightest, even if the show tries to put on a new perspective. She could act the way a 21st century woman or a man would, blissfully unaware that this is causing turmoil for the fragile 19th century souls. That's, of course, not how the Doctor ever acted, and any historical situations would hardly be a match for Eleventh's performance at the start of The Time of the Doctor.

I'm slightly disappointed there's no naïve companion to deal with her regenerating this time. I began Doctor Who with binge-watching the Ninth,* and I didn't know the Doctor regenerated, so my disappointment at the Tenth's appearance rivalled Clara's welcoming of Capaldi. I think a gender change would have made that all the more hilarious. Although slightly cruel, as Clara definitely had a crush on him.
* ENT: Future Tense brought me here!