I guess my first question is much do you like/love this girl, and how much does she love you back?! It'd suck to spend $600 on her to buy her a gun just to have her cut and run on you with your former best friend!

Seriously, though, why not consider getting her a slightly less espensive gun for her to use for awhile while she gets her feet wet? I'd recommend the H&R/NEF Pardner single-shot rifle in .243Win or 6mm Rem, and spend a little more on getting good glass for it. The NEF's will shoot as well as most factory rifles, are simple to operate and maintain, safe, lightweight, and you won't cry when you have a 'smith cut down the stock to fit her frame.
I personally would lean toward the 6mm Rem if the NEF is available in it, but I'm a handloader so ammo selection/availability is a non-issue for me. If you plan on relying on factory loads, the .243Win ammo is plentyful, cheap, and offered in a wide variety of load/bullet combinations.
The added advantage of the NEF/H&R is that if later you decide to put a ring on her finger and a bun in her oven, you've got the perfect rifle right there to start your new little hunting buddy out on when s/he's old enough!
Mike