It would be very difficult. Not only in convincing the fans that this is still the Doctor we know and love but in that writing female characters with 'extreme' personalities is very very tricky. A female Doctor might need to be a more mellow Doctor than we've seen of late. As a rule, people tend to be more forgiving of undesirable personality traits/quirks in male characters (arrogance, for example). I base this entirely on personal observation though, mind you.
I'm not certain it would still be 'Doctor Who' as we know it, but I'd still watch.