Cz527 in .222, .223, or 7.62x39
If she's serious, then a Saiga in any caliber other than .308 would be a good fun pick.
I'll talk from personal experience here. I was a kid who was still learning how to shoot not even 8 years ago.
I really don't think that the 22lr phase is necessary for shooter development. I don't see the point of making a kid use a single shot iron sight 22 for hours on end, making tiny 25Yd holes one shot at a time, adjusting the sights in between shots and working on absolutely perfect technique. You'll bore the kid to tears. At least make sure that the thing has a magazine and that she learns how to cope with recoil. The first gun I ever fired was a full-sized 12 gauge semiauto firing some pretty stiff loads. I don't recall one kid moaning about recoil or weight.
Kids outgrow genuine child guns quickly. You give a 9 year old a kid's Cricket, and come Christmas next year, the thing's become like a mare's leg. Children are far more capable of using proper adult guns than many give them credit for. Heck, once I got shown how to handle the 12 gauge recoil, I didn't have much trouble, weighing in at a measly 95 pounds and 56 inches at the time.
One of the hardest things to do is to keep kids interested in doing something tedious that they perceive as being perfunctory. I hated doing the 22's as a Boy Scout because all it involved was going prone, then taking a quarter hour to fire five rounds, each loaded one at a time. Did it teach me much? Yes, but I didn't get nearly as much benefit as I could have because there was a wrong emphasis on perfect form versus actually doing anything interesting. If you make something fun, then kids will follow it and become proficient. If it simply isn't enjoyable, then they'll lose interest and go elsewhere.
