In my opinion, restringing might give her a bit more control and consistency, while also giving her something "new" to play with. I remember at that age getting anything new...grips, shoes, etc...would up my excitement for a few days, and make me a bit more serious about my game. But I think Natural Gut is a bit too much. I remember being that age and doing all sorts of bad things to my rackets (like hitting wet balls, or rocks, or really whatever I could get my hands on) when I was bored. It would be a shame to ruin an expensive string job doing something kids are prone to doing! Also, I don't think she would notice any difference between a synthetic and natural gut at her level.
Plus, syn gut comes in all these cool colors that are more fun for kids than boring old tan Natural Gut! And, she presumably doesn't have any elbow, wrist, or shoulder problems that might necessitate NG. Go with a 17 Syn Gut.
So, give her a new, fun string job and she'll feel like a little pro! I also don't agree with the earlier blanket statement that advised you not to re-string any pre-strung racket. There are quite a few mid-level rackets that are pre-strung that are more than suitable for being restrung. Yes, some cheap rackets are made with the expectation that they will never need new strings (in fact, stringing them would usually cost more than a new racket in that class). But to say that across the board it isn't wise...that is just too simplistic of a statement.
