Chicken Charlie, if somebody told you that you were "cheating" by tuning a baritone uke that way, he/she was uninformed. Melani is correct: DGBE is the standard tuning for a baritone ukulele.

I'm not an expert on guitars or teaching guitar, but I do know a bit about child development (and I have a 7-year-old daughter who is very musical). I would agree with Kaleea that if your daughter says she wants to play the guitar and you hand her an ukulele or a mandolin she may be a little disappointed or confused. At 7 she is old enough to know what she wants, and I think it is a good idea (and beneficial to your relationship and her self-esteem) to honor that if possible. The half-size guitar sounds like the way to go. Definitely nylon strings, and definitely a good quality instrument. It's understandable, but unfortunate, that most people buy cheap instruments for their kids to learn on. If purchasing a good instrument is not feasible, you might check into renting an instrument from a reputable teacher--not from a music store, where rentals may be fairly low quality (though I'm sure there are exceptions, and you have to know your local resources). Good luck--and enjoy! Unfortunately my daughter lives far away from me, so I don't have the joy of playing music with her--yet.

Aloha,
Mark