I would suggest the Model 7 from Remington but I'm sure all the other major manufacturers offer a similar youth option.The .308 is fairly tame as far as recoil goes, but if you are worried about recoil you could go down to .243. Much tamer recoil but still adequate for deer.

This might be obvious but I'll say it anyways, recoil is 90 percent mental. When you teach her to shoot make sure she keeps the rifle snug to her shoulder and use good form. Also make sure she has good hearing protection. If she shoots a rifle and it rings her ears, comes flying back into her shoulder and gives her a scope cut she is going to think a .308 has nasty recoil. If she has good hearing protection, has the rifle snug to her shoulder, and keeps her head a safe distance from the scope she will go "oh that's not bad at all"