In reply to bigalxyz:
I'm sure there are tonnes of suitable guides and courses in the area, and really almost all of them seem to offer a day or half day outdoor "taster" option, and are happy to arrange something for one or two people. So you're going to be spoilt for choice.
But off the top of my head, I know Mandy Glanvill is based in Cumbria -- I've climbed with her in the Pinnacle Club and done her self-rescue workshop, and she's lovely, very sensible and steady (and I say this as someone who can be on the anxious side myself):
http://womenrock.co.uk (despite the link title, she does take mixed groups so it's not a problem if you're not a woman! *g*)
http://womenrock.co.uk/control.php?page=activityDetails&activity=taster...
> Probably next Wed/Thu.
A suggestion: if you can't arrange something at short notice, how about giving your daughter a "voucher" for it, like a card and a written promise that you'll arrange a day/half day for you and her to go on an outdoor taster session together at a time that suits her?
Also, I just wanted to say what a lovely and thoughtful idea it is, and that I hope your daughter has a great birthday.