We were just in Disney in December and dealt with this issue. I have two children, ages 8 and 11, and my wife, all of whom have wheat/milk intolerance/allergy issues. We called WDW Dining beforehand, and they sent us (by email) a complete list of all counter locations within all parks and resorts which featured wheat free/milk free items, as well as provided a list of places we could find milk alternative / wheat alternative products (like Tofuti ice cream - soy based or wheat free rolls).
When we made our ADRs for the restaurants, we also had a note added to the reservations indicating the allergies and at each restaurant the head chef came out to the table, introduced her/himself, and reviewed all of the items on the menu which the kids could eat. At Hollywood and Vine (in DHS) the chef even took the ladies down the buffet line and reviewed every selection on the lines with them; she even made them special wheat-free rolls and special dessert. My kids felt like royalty.
New Year's Eve was my wife's birthday, and we have made reservations for dinner at Cinderella's Royal Table. I called dining and even arranged (in advance) for a wheat-free/dairy-free birthday cake which was AMAZING! Tasted just like a regular birthday cake.
In short, don't let dining issues block you from enjoying any part of your Disney experience. Just call WDW-DINE in advance and let them know your restrictions and issues and they will do everything they can to accomodate you.