I have a Savage Model 111 GCNS in a 7mm-08,Bolt-action with the wood stock and the Accu-trigger and its a great gun and it has a lighter recoil then a .308 or 30-06.Another thing You can do is to get the Remington Managed Recoil shells if You get Her a Bolt-action Rifle,the MR shells are great for less recoil and as Your Girl gets older She can change over to the regular shells and the point of impact on the regular shells won't be far from the other managed recoil shells.

As Cuda67 mentioned the .243 is also a very good Rifle for a Younger Hunter and I also use one too for Hunting Whitetail Deers!