This just my opinion.......a.) she does not need a handgun, at least not till she is a very proficient rifleman. b.) NO Scope on the rifle till she has mastered open sights (This should require 2 to 3 years). I would avoid self (auto) loader rifles. If your hunting you only need one shot. My first choice would be a "High" Quality bolt action rifle in .22 Rim fire. The CZ-USA line is my first choice (I own (5) CZ-452's and (1) CZ-453.
If I had a son or daughter I would buy them this firearm because it has a wonderful sight system, and I would cut the stock to the proper LOP for her. She can shoot it for years with no butt plate. and later in life when she is fully grown she can add a butt pad................
http://www.cz-usa.com/products/view/...raining-rifle/
I would buy two extra magazines also.