For an 8 year old girl...hmm. I'd say MAYBE move her up to a .223, then eventually a .243Win as she grows a little. But everyone's recoil sensitivity is different. My wife, for instance, won't shoot more than 20 shots in a session with our 22-250 before she starts feeling the unconfortable effects of recoil, but I can shoot it all day without bother. My wife is probably a fair bit taller and heavier than your daughter, too(if I posted her weight here and she found out, she'd clean my clock with a frying pan, so I won't mention specifics! ). I wouldn't try to move her into anything to big too fast, because a sore shoulder isn't going to make her want to shoot anymore. Too much recoil would also likely lead to her developing a nasty flinch which might be very hard to cure and seriously compromise her shooting.

Is she even old enough at 8 to hunt yet? In Iowa the minimum age to hunt is 12 I believe, but Wyoming may be different. I would say that if she can't even hunt yet, there's no reason to have he shoot a more powerful rifle. I'd just stick with the .22LR, or maybe even get her a nice little scoped .17HMR. The HMR's have a more 'grown-up' feel than a small .22, and they are good on a calm day to 200 yards. Wickedly accurate too. Savage sells their bolt action .17HMR for between $220-250. I almost bought one today for myself. Gander Mtn has them on sale for $219 with 4 boxes of Hornady ammo free with the rifle.

Mike