Well, friction is a temporary method that removes the portion of the hair above the skin's surface, so it is not permanent. It should be safe to use on her legs but I would definitely recommend adult supervision at all times, and start very gently. Be even more careful if you are going to use friction on the back and arms, and I would not recommend friction for the upper lip.
You might check the Hairfacts site and other Hairtell forums to help determine which methods would be most appropriate for which areas. The only permanent methods are electrolysis and laser. Laser is effective for dark hair, but it should be used with extreme caution on dark skin because it is more likely to scar dark skin. And I don't know if electrolysis or laser would be recommend for a child so young. Hope you find something that works though.