Absolutely. Table service restaurants are fantastic when it comes to g-f options. In fact, I was so sick of creme brulee or flourless chocolate cake our next to last night at WDW last time we were there that I whined to our server at Citrico's about being really tired of either of those for dessert. He laughed and offered to ask the chef what I might have instead. I got a soup platter piled with fresh berries with a huge dollop of whipped cream. Absolutely deelish!
Counter service is relatively easy, too. They have a book which lists ingredients for everything sold. Some CM servers may know what menu items are g-f, but if not, ask if the ingredients list can be consulted to see what things are.
You'll also find some snack items at the resort food courts, too. We had leftover snack credits, and I ended up taking home 3 or 4 bags of Divvies caramel popcorn. Yummylicious! From what I've seen reported on PP, there are fewer g-f snacks available than previously, but you'll still find some things that are.
Just be sure when you make your ADR's that you specify that you have someone in your party needing gluten-free meals as well as telling your server that when you are seated. You may even find if nothing on the menu appeals that the chef will agree to make something special for you. WDW is fantastic where special dietary needs are concerned!
"Too many people grow up. That's the real trouble with the world, too many people grow up."--Walt Disney
Gluten free dining is just a bit different at DLR than at WDW. Table Service restaurants are much the same. The chef will come out and visit your table and go through your choices and options. Reservations can be made 60 days in advance, be sure to note your dietary needs on the reservation. For Counter Service you can pick up a list of eateries with choices (most places have something) at City Hall on your way into the park. This list includes popcorn carts, etc. You can also email DLR.special.diets@Disney.com with questions and concerns. I've even had a chef email me directly. If you scroll down a bit in this forum, you'll find a gluten free dining review of one of my recent trips.
Don't worry, you'll have a wonderful visit with delicious and safe food!
Our last trip was the first one where my daughter had to eat gluten free. It was wonderful! We didn't have to worry about her getting sick while we were there! She loved just about everything she ate and loved all the options! Best of luck! I'd be happy to help with any gluten free questions you have! My daughter was diagnosed with Celiac Disease about 5 years ago. It can be absolutely overwhelming! Just PM me if you wish. Best of luck!
Gluten free for about 9 years now. Disney (Land or World) is great for gluten free dining! I can't add any more to what's above, but you won't have any problems with finding food.
(I would recommend Redd Rockett's Pizza Port in Tomorrowland for gluten free pizza. You have to ask for it at the counter, but they make it only after you order it. I'm the only gf person in our family, but my family ate my pizza and said it was far better than what they had!)