I have celiac disease. I pick up the gluten free list at city hall when I go. Most of the sit down restaurants didn't have a gluten free menu, but it said to talk to the chef. I only tried this at Ariel's Grotto, aside from that we had counter service.
Ariel's Grotto was wonderful. The chef came out and we discussed the whole menu. I wasn't able to eat the bread on the appetizer tray, but there were things I could eat (cheese/fruit). Then I had a salad. Then they brought out my entree. It was some chicken dish, I don't remember anymore, but it tasted very good. The dessert tray was not gluten free, but the chef had them bring out some freshly made orange sorbet so I didn't have to miss out on dessert either. Plus, the entire time my daughter got to meet the princesses. I'm not sure how old your daughter is, but if she's in love with the princesses it might be a good option. They were definitely able to accomodate me there.