Disney is wonderful with accommodating food allergies. I've enjoyed many gluten free meals there!
The quick service choices are safe and taste good, but they will be more sandwich/burgers/ salads, etc. Stand out quick services for me are Flame Tree in AK, Sunshine Seasons in Epcot and BOG lunch in MK (roast beef on millet bread). I also find great choices in Epcot during Food and Wine and Flower and Garden. They have the gluten free options listed on the menus.
I would recommend that if you can spring for it, try at least one or two table service meals. Those are where Disney really shines with their gluten free options. My favorite table service restaurants are: Raglan Road, DS, (gf fish and onion rings are amazing!), Bongos, DS (skirt steak), Sanaa, AK lodge (bread service and butter chicken), Biergarten Epcot (buffet- we visit each trip), Spice Road table, Epcot (rack of lamb, mixed grill skewers), O'hana breakfast, Poly (mickey waffles, eggs, potatoes). Table service lunch is usually cheaper than dinner.