My wife Choose a Left hand Browning X bolt micro hunter in 7mm-08 when she started hunting. (Totally her choice) When the oldest daughter turned 12. She got the Savage Axis youth in 7mm-08. As the oldest boy turned 12 he got the TC Venture in 7mm-08. At that point I was feeling left out so my wife bought me an AR-10 in 7mm-08.
In my opinion it may have a more recoil than the most timid shooter might want, with full house loads, but it's a great choice for the average beginner. My third oldest son was more interested in bow shooting then noisy kicking guns. We put him in for an antelope tag and he decided a rifle was the way to go. I loaded some 120 gr bullets with just enough powder to cycle the action of my AR for him to practice with. He likes to shoot the rifle now. He only shoots 6 to 10 rounds a session and then he's had enough. I think the 7mm-08 would be very versatile for her if you want build it up for her as an adult. A 260 or 6.5 creedmore would also be a great choice. If deer is the largest thing she will ever go after then the 243 is a good choice too. Fast 22's kill deer with the great new bullets available now but they are in the barely adequate category, IMO, and are still illegal in some states for big game hunting. Any of the larger rounds mentioned would definitely give her more room to grow.