I have a dairy allergy and we had a great breakfast at Cape May because they had the babycakes donuts and cupcakes available.
However, last trip we ate breakfast at O'hana and I think that has been my favorite breakfast ever!! DH (who is not allergic to anything) said that next time we eat there, he's going to tell them he has an allergy just so he can have the food, too! LOL Everything was just really fresh and IDK it's probably the same waffles and everything everywhere but for some reason it was just really good!
My cousin's BF also has an dairy allergy and it was his first time at Disney. He LOVED it because there was always something new for him to eat without worrying!
They have dairy free waffles at almost every quick service place at the resorts and some places have even offered DF pancakes. I did have the DF Tonga Toast at the Poly and it was so, so good! They also make DF beignets at French Quarter. Last time I was there the Dole Whip was DF so you could check that out, too.
I can't think of any special desserts I've had. We usually go to babycakes to get cupcakes and such so I'm sad they are closed now.
Some places have Rice Dream / Tofutti / fruit sorbet. It's not very amazing (but was amazing to a person who can't ever go anywhere and get ice cream) but at Beaches & Cream I was able to get Rice Dream Vanilla with chocolate Hershey's syrup, peanut butter and chocolate sprinkles! IT WAS SO GOOD! So definitely check that out while you're there, I'm sure they can make him something good!
Oh and the allergy friendly chicken tenders that they have throughout the parks are also fab. DH loves them too!