First of all it helps to know the extent of the allergy. I am on a no wheat at all diet due to celiac so I will not eat in pizzarias because of cross contamination. On the other hand I have on problem with being around or touching eggs and soy but they are on my allergy list.
Allergies can be unrelated like my soy and eggs or come in families like hazelnuts and walnuts. Peanuts are legumes thus they are not that closely related to tree nuts.
First read the stickied FAQs for this board.
http://www.disboards.com/showthread.php?t=595713
Here is a list of menus at this site. They and all ears are pretty similar. This one has a search engine so that you can find by location, type or even keywords like popcorn and bacon.
http://www.wdwinfo.com/wdwinfo/dining/diningmain.cfm
http://disneyworld.disney.go.com/wd...etaryDetailPage&CMP=PAC-WDWSpecialDietsVanity
This is the official site and its dietary numbers to contact. You contact them and they will send you a list of foods that are for your allergen. On any reservations you need to tell them of the allergies. For ice cream parlours you can ask for clean dishes, new tub of ice cream, and a new scooper by just saying that you have an allergy. At buffets the chef will walk you through the line and if you are worried about cross contamination the they will bring out new pans. They can also make special plates of food for those with very special diets.
counter service can be a pain if you do not do your research ahead of time. The menu's and some of the info on this board will give you an idea of what is served at the parks like Edy's/Dreyer's ice cream, Morrell hot dogs, divvies, Vans waffles, Itszadoodles, heinz ketchup, and Dole Whips. When I go to parks I know that I can have ice cream but not certain flavours for example.
I have read every menu in DLR at least twice and when I go next month I will know where I can eat and what is available and any delays because of my wheat reactions. I know where to get hot dogs and dinners. The same is true for people with special diets and allergies on either coast. If you get a snack attack you should be able to look at your map and say where are good snack spots. I do not need a map as I got it down pat in my brain somewhere and know the park by heart after 47 years going to DLR over 200 times.