Very cool image with female versions of all doctors: http://doctorwhotv.co.uk/wp-content/uploads/the-female-doctors-300x421.jpg
It would be kind of fun if they did do a story where the Doctor's Tardis somehow wound up in a reality where well... he was a she and his/her choice in companions changed or maybe stayed the same, but it was a different dynamic. While I don't particularily see a lesbian Doctor, I could see him having a motherly/sisterly relationship with some of his companions. If anything the most 'Butch' would be 9 - not really wanting to be a mother figure or sister. 10 I could see being a bit more sisterly/best friend with Rose. 11 she'd just be quirky and awkward and geeky and maybe a little more friendly rivalry with Amy. River Song would probably still be her 'wife' - she looks like she could swing either way LOL
Thanks Mr A. Havign the Doc slip into an alternate reality and meet his female self might be fun. Heck, it might be a cheap and interestign way to do a multi-Doctor story.
So thinking of actresses - who'd be close enough physically and personality-wise to any of the previous (or the current) Doctor?
Five is really cute! And Eight has that lovely Victorian-era charm (I'm thinking Ruth Bradley in Primeval).