First off it depends on the type of allergy but this is my general guide to allergies.
Bring wipes and wipe down eating areas and chairs to make sure some gummy handed adult has not left left there finger prints on salt and pepper shakers, sugar compartments, under tables and counters, on the chairs, and on the tables. I have a bad habit of eating things off of my kitchen counters when that is dangerous as mom's cookies or bread may have been on the counter.
As stated above contact the special dining people. They will send you a list of allergens related food information. You can also at times look up foods that are commonly used at parks like Dryer's, Edy's, and Nestle frozen treats for example. Fruit Bu is being sold in DLR now and a person can go to the Fruit Bu site to check on allergens. Dole whips have soy, casein but not dairy for example.
At DLR I told the waitress that I was gluten and soy free. The chef came out and started walking me through the menu and we stopped at tri tip.

I got blood orange sorbet for dessert while the others ate chocolates. ARGH. The second time this week I told the lady who took my same day reservation about the gluten. The chef came out and talked to me about the menu even though I knew what was safe. The same thing will happen when you set at WDW table service restaurants owned by Disney. San Angel, Yak and Yeti, Rainforest, Hard Rock, and the food court at Coronado Springs are not run by Disney. Yak and Yeti and Rainforest Cafe are out of the T-Rex owners Landry. Disney is very good about allergens except them idiots at the cone shop at DLR. WDW has the land and more guests so they are way better able to serve guests with dietary limitations.