I believe you need to contact Carnival and let them know of these allergies so they are prepared. I noticed on the e-docs for the Camp Carnival there was an area about food allerigies so make sure you also complete that portion.
I think it is going to depend on what a picky eater he is and exactly what he can and can't eat. Definately call about the soy milk, I have never seen any but it may be one of those things you need to ask for. Also, make sure you talk to your waiter...most of the kids items are going to have some sort of milk it it with the cheese and such, I know they don't have soy cheese. There are plenty of vegetables and meats and starches and stuff and you can specify with no butter, etc. He may just have to eat off of bits and pieces of the adult menu.