Short answer: At least a month in advance of your arrival.
I am assuming your son has allergies, but I know that might not be the case. We've spent quite a bit of time at DW with a child with multiple allergies (dairy, egg, tree nuts, and peanuts) and have always had good luck with both table service and counter service. Our first trips to DW special diets seemed more helpful. During our 2010 and 2011 trips not so much. This was not really a bad thing for us because we were so well taken care of at the individual restaurants. That being said, I see you leave in a little over two months, I think it would be okay to contact them any time between now and about a month away. They will give you enough information to get prepared for the trip. They will on request send you a dietary reference sheet for quick service items. I just noticed that it was last update in March of '08, so always ask whether the food item is okay.
For us, the most important thing is to let the server/host/hostess know about the allergies and they will let the chef/allergy specialist know to come meet you and discuss your allergies. You can also note them in your ADRs, but we have found that we have to provide that information again. If the allergies are numerous or rare, you'll need to let the restaurant know in advance. The same goes if you have a specific request.
If you have any specific questions about procedures, restaurants or specific allergies, I'm sure you'll get a lot of information posting here.
I hope your Disney vacation is wonderful.