We're supposed to believe that he was a ken doll, and then spontaneously made himself a penis after meeting her? I'm sure he could handle the coding, but the Doctor is programmed to be contentedly cockless.
Denora being a real person, not so much.
(Sans moose knuckle not baloney pony. Get your head out of the gutter.)
"This is all fine, thank you for rescuing me, you're all wonderful, but how come I don't have any sexual organs?"
I'm assuming that sex with holograms is common place, and Zimmerman didnt' want to see his program drafted as a sex worker when he's supposed to be Doctoring.
The Doctor made her business which was his inspiration in defiance of his own programming to generate his own business.
But there's an erudite theory closely related to Godliclocks a nd the three bears that for every vagina out there there is the perfectly sized penis, not too big, not too small, but perfectly complementary, a package that elegantly fits in the box, and that's what everyone is looking for, not a sense of humour, not a nice car but something sexually complimentary. The right tool for the job.
The Doctor built both tools. Unless he was an idiot and ignored making it feel like a key sliding into lock because threading a chicken sausage down a bendy straw seems appealing to his fauxmachismo, he could have hypnotized her with unexpected simpatico of his goldilocks johnson.