We've visited WDW a couple times since needing GF meals for myself and 2 of my kids. We found WDW to be great for GF dining, but you will need to plan in advance. Contact WDW and someone there will send you loads of info on what to do.
theresa.joiner@disney.com was the person that I dealt with. She sent a bunch of docs that gave lists of good restaurants and products that would likely be on hand, and which ones need advance notice.
One overall word of advice about counter service - don't go at busy times. You'll have to speak with a manager before they'll put in your order and it might take 15-20 minutes for them to be able to get to you.
Restaurants that we tried and loved:
Crystal Palace buffet - the chef walked us through the buffet and showed us everything that was safe. My friend and her kids can't eat gluten OR dairy, and they were also thrilled with the Crystal Palace buffet. We went to the lunch seating.
Pinocchio Village Haus - pizza is Amy's and the manager definitely understands celiac. They have a dedicated oven so it takes longer to get the pizza, and you'll have to cut the pizza yourself since they don't have a dedicated pizza cutter.
Cosmic Ray's - burgers and fries. My daughter LOVED having a burger with a bun again!
Le Cellier - fantastic meal with chefs that really understood celiac
Mama Melroses - same as Le Cellier
California Grill - ditto
American Adventure in Epcot - burgers and fries
Seasons in Land Pavilion in Epcot - salmon entree
Disney also will let you bring in safe snacks for yourself. They have lockers you can rent to store them if you don't want to carry them around.
WDW is one of the best places to go for vacation if you have dietary issues. Another member in our family is vegetarian, and it was such a relief to always be able to find food for everyone! And my GF kids were thrilled to be eating foods "just like other kids" while out at an amusement park. We've tried traveling other places and it's such a challenge.
Terry