Depends entirely on her. At her age and experience in other shooting sports I'd say she's likely ready for a 20, at least a gas semi-auto. And with a 20 the pattern is sufficient to go 25 on a standard trap range if the shooter does his part. At 4-H we'd move her to a 20 ga. Remington 1100 Youth Model (club guns) and see what happens. Or the little Franchi semi-auto which with the aluminum receiver is lighter. Weight can be a bigger problem than recoil. At that age arm/shoulder strength is generally yet to develop, particularly with girls. Keep in mind that with gas guns felt recoil is roughly 1/3 of a locked action and are as safe as any loaded one round at a time.
Fit on the youth models may not be competitive trap shooter perfect but it is plenty close enough for the standard size shooter at less than a seriously competitive situation.
We have a Rem 870 in 28 ga. with a cut down stock on loan from one of the instructors. I don't like it, recoil is about the same as the 20 gas guns and balance is poor. It does work well for some of the recoil shy bigger shooters where the fit makes more sense.
Do stay away from the single shots, by and large they are horrid. I've seen bigger kids that could easily handle a 12 ga. 11-87 give up in the middle of a round because of felt recoil with the light weight and poor stock design.
Look for a mainly social youth shooting club, hopefully with good, certified instructors. We run our local 4-H Shooting Sports trap that way and 4-H clubs are supposed to do that but some lean on competition too much. With us we'll coach and encourage competition if the shooter wants it. If you just want to shoot for fun with friends that's perfectly fine with us.
