I have a 10 year old daughter that has dark hair on her upper lip. She has asked me how she can get it off. I am not sure how to go about removing it at her age. Any advice would be appreciated.
Only Electrolysis is permanent, but you must find a well qualified practitioner to do this work.
Of course, since you failed to enter your location information in your profile, we are unable to direct you on who might be good in your area.
I would also look into anything that might be making her grow excess and/or dark hairs, so that if there is a way to stop something in its tracks, you could do that before any real trouble came up.