My DS 2 is allergic to eggs and peanuts. While I have not yet been to WDW with him (June 2010!), below I will give you what I have learned from Intercot on this issue.
As difficult as it is for me to do, you will ultimately just have to trust that Disney will make it work for you once you get there. Going through menus and trying to determine what has milk/eggs and what doesn't will be almost impossible unless you email a chef at each restaurant with specific questions for specific menu items. Even then, menu items may change before your trip arrives, so planning ahead is hit-and-miss at best. While I did email my most concerning restaurant (Tony's) with direct questions, I finally decided to just trust that Disney will do just fine. The Chef will make it work once you are sitting at the table.
For buffets, Chef's will usually ask you what you want off the buffet, then go and cook a special batch just for you so that they KNOW it has not been cross-contaminated.
For counter service and snack locations, most places should have a book right beside the cash register which lists all ingredients in each food they sell. Some counter-service managers will know this information by heart, while others will have a hard time remembering where the book is kept. You can get some information from Disney by sending an email to
[email protected] and asking for information on food allergies. They will send you an email with four files attached, and one of them is a list of allergy information for some of the more common (and standardized) food items at counter service and snack locations.
Below is a thread I started with a lot of information packed into it. It contains a trip report from someone with egg & peanut allergies, a detailed list of what you can get from the special diets email address, and my experience with emailing the Chef at Tony's Town Square.
http://www.intercot.com/discussion/showthread.php?t=162703
Good luck to us both!