Have your daughter sign up for a State Firearm Safety Training Class. That I would suggest be your and her's first plan or hurdle to accomplish before buying a firearm.
Depending on how her body build is for stock length. If I were in your situation OP I would have her measured at a well known local gun shop to see if she could handle a T/C Encore. Its a single shot rifle. But everything including its stock, forearm, and barrel, can be interchanged as she grows. If you have a 22 rifle to start her off target shooting with >great. Otherwise if money is not in short supply. Get the Encore ordered with a 22 barrel w/ open sights. Right off the get go. Then purchase another barrel for that Encore. Something more appropriate later down the road to hunt them piggy's with after your daughter has had some range practice first. Learning how to shoot with a 22 is far and away cheaper than doing so with a center fire rifle. That's how I would proceed with my new hunting pal if that occasion ever arose for me.
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