My son has a life threatening Peanut/tree Nut allergy. We travel to Disney every year. We have found Disney to be wonderful about it. We had great experience at, Le Cellier, Rose and Crown, Crystal Place, The Plaza, Garden Grill in The Land. Sci-Fi, MaMa Melrose.
I would not recommend Wolf Gang Pukes on the West side at DTD they use alot of peanut products. Even though they were GREAT, about it while we were there I was a mess with worry, but he assured me he take every precaution there was, and he did. Nothing came to our table that was not safe.
We stay away from AK meals and Mexico and Chinese.
All buffets we had no problems with, the Chef comes out and walks us through it or they brought out different food for him.
As long as you let them know, you will be fine. Remind them when you get there at check in and again when you order.
Good Luck Maria