^^ What upnover said. I'd also ask her what she plans to do with the horse - what her goals and aspirations are... if she claims to just want a "trail horse" but has dreams of jumping, well you can bet your horse will be out there jumping on the trail
Also lay ground rules for taking your horse off of your property, or to shows/etc. What tack will she use? A "test ride" is a must IMO, references are good, too.
Also, I would be ultra nosey and ask about grades at school (that will tell you a lot) - plans after school - and ALWAYS meet the parents (they'll have to sign anyway). If you can, ask/find out where the money will be coming from - will she be responsible for making the money/paying you, or will it come directly from mom/dad?
Good Luck :)