Do you expect the house to sell at its current price OP?
Re: "girly stuff".
You can do this. If your wife had died you would, right? You wouldn't just palm DD off on your sister/mum.
By "girly stuff" you could mean a number of things:
Menstrual problems
Other gynae things
Dynamics between girl friendship groups in school
Whether she should use Rose Raspberry or Frozen Winter on her nails
First 2, you encourage her to use specific biological terms, then you take her to the GP if needed. So "My you-know-what is thingying!" is out the window - she needs to be able to say "I'm having a period and it's really incredibly painful/I'm bleeding way more than normal/My vagina is itchy" If she's uncomfortable with saying it to you then you can facilitate a GP appointment with a female doctor. Sit in the waiting room and tell her if you want her to come in then just call you. (Just in case she needs referring.)
No 3, tbh I don't know, i was shit at this stuff at school and glad I didn't have DDs. I guess this is one you'd ask her female cousins to talk through with her. Or teach her how to lay a sucker punch
No 4, this is trivial and something she doesn't need a parental figure for, she can just discuss with friends. Yes it's nice sometimes to have your mum do your hair or nails but it's hardly a crucial part of parenting.
Good luck on your date but please don't make the mistake of staking all your emotional hopes on one person or trying to fit a square peg into a round hole. (hurr hurr) Just have a nice time thinking "Yes this could be my future, meeting women in pubs, having an intelligent conversation and eating good food." Please don't do the rebound thing.