My sister has celiac's and I'm gluten-free, too, we dined gluten-free at:
La Hacienda de San Angel - Epcot - most of the food we ordered was naturally gluten-free, but they also added some corn tortillas to the cheese appetizer for her
Cape May Cafe - dinner - they had minestrone soup on the buffet that night, but they prepared some soup without pasta in it just for us; there were lots of gluten free options on the buffet
Columbia Harbor House - the chicken tenders were gluten-free and very good
Captain's Grill at the Yacht Club - breakfast - twice - one morning they brought me gluten free toast (Udi's) and the other morning they made gluten free Mickey waffles - I think all the restaurants that make Mickey waffles will make gluten free ones. I've had the gluten free waffles at Roaring Forks at the Wilderness Lodge
I've had a gluten free meal at Ohana's - they prepared gf chicken wings that were delicious, along with pork, rice and broccolli. The dessert was an ice cream sundae with gf chocolate cookies.
If you are going to be in WDW during the Flower & Garden Show, you can get a list of the gluten free items in the food booths.