Disney has been excellent with dealing with food allergies. Our daughter has tree nut allergies and even at the buffets they accommodate her. I would imagine that a Gluten free diet would garner the same attention.
As for a nice restaurant for an anniversary dinner and your wife's dietary restriction, I would recommend Citricos. We went for our anniversary a few years back and it was great. I cannot eat garlic, which like a gluten free diet, can be tricky since every chef uses garlic to a certain extent in almost every dish. However, the chef came over and talked with us for a while and pointed out the items that I could eat, and even offered to make a dish that had garlic without the garlic. So that was a huge plus for me.
Aside from handling my intolerance to garlic, the restaurant was outstanding. It was as good as any big city fancy restaurant, and I found it to be a great spot to celebrate an anniversary. If you tell them it is for your anniversary when making reservations, they may print up special menus with your name and anniversary your celebrating on it. (I know there is no guarantee for such things, but they did it for us.)
Good luck!