I think the people guiding her career need to be patient. Unlike the golden days of Hollywood musicals, there are few places for youngsters like that to get the professional mentoring and showcasing they need. If I could advise the girl and her parents, I'd say let her be an ordinary schoolgirl for at least four more years, until she reaches 16. Let her do school productions; maybe do local theater if a musical is playing that calls for a young girl vocalist. Keep an eye on upcoming Broadway productions that might have young girl roles, and try out for them. Mall concerts are also a good training ground.
All of that would be excellent preparation for the kid to learn the ropes, learn who she is musically, and simply mature.
Either that, or if the kid can act, maybe she could try out for non-singing roles on TV and other productions that need children. That would give her the exposure and connections she needs to try for a singing career a few years from now.
I think you are absolutely spot on. I just hope they don't ruin her career by trying to push her too fast.