This is a very common question for many parents. They are concerned about letting their pre teen or teenage daughter loose with a razor which at the end of the day can and will promote more hair growth.
The problem is some young girls do have some hair, and once they hit around 4th or 5th grade (Almost always by 6th grade) most of the other girls are shaving. So when it is noticeable that she has some hair there other girls can be quite nasty about the name calling and picking. Shaving the legs is often looked at as a adult thing to do.......and if she is not doing it then picking almost always takes place.
Since its such a little thing we often encourage parents to allow it once the child is at least 11 or 12. Though if your daughter has more growth then average its better to start a little earlier. The fact is her self esteem is far more important then the age of when she should start. Allowing her to feel confident about how she looks and feels is always more important then the little things.
What I would suggest if she is under 13 is allowing her to try the Veet program. (Can be found in the razor isle at your local stores) It is a cream she can apply and use a stick (That looks a lot like a razor but has no blade) the stick will remove the softened hair and give her a closer removal then creams alone. This gives her plenty of practice learning how to handle a razor (Without the blade) and removes the hair.