There's places that you can get an adult portion of a kids meal. Not everywhere will do it though. However, with all the tools available, most people do a little research to see what they and their families would eat ahead of time, to see if going to that restaurant is even worth it. You wouldn't go to somewhere that only offers seafood with a member of your party who is allergic to it would you? So do yourself a favor and make sure that you have a worst case scenario ready that if denied the kids menu, your kid is able to eat something else from the adult menu.
If your child (or anyone for that matter) has an allergy, it's best to put that on the reservation notes when making the reservation. Allergies aren't a leverage tool for getting your way if the servers say "no". This is how things get abused. Sure, you may get your way once, but rest assured, that manager answers to someone as well. They all talk and if it gets abused, things change. Also, what would you do if they couldn't accommodate the allergy? Disney is one of the best places for having allergies accommodated, but they're not perfect.