Hey Tammy,
I also have a child with a milk allergy (and many other food allergies as well), and we went to
Disneyland with her for the first time in September last year. I was really nervous about the food situation, but we managed to make it through the week without any allergic reactions.
I did call and speak with Chef Chris and he was great. My daughter was celebrating a birthday down there and we arranged to have the Disney bakery make her a milk-less cake. Any of the sit down Disneyland restaurants will send the chef out to your table to discuss your child's food allergies with you, and they can definitely special make a meal for you if need be. They were more than accomodating.
As for the counter service restaurants, I was advised by Chef Chris to ask to see the ingredient list for the particular item you would like to order. It is not enough to ask a person working the counter if an item contains milk or not. As you are aware, there are SO MANY terms that mean an item has milk in it (whey, caseine, etc.) and people without milk allergies don't always understand that. If they don't see the word "milk" in the ingredient list they assume it is safe. So, he said it is best to read the list with your own eyes.
If you are staying at a local hotel, you can always visit a grocery store near by when you arrive and go back to the hotel for some of your meals. We had a microwave and fridge in our room so that was a blessing for us.
As for restaurants off property, you have to be VERY specific with what your child can eat. We would advise of our daughter's milk allergy, and then they would arrive at our table with a hamburger with butter all over the bun!!! Yikes!
We also packed allergy-free snacks for our daughter to eat while in the park, and we actually found some milk-less snack foods in the park (the little frozen minutemaid lemonade and pink lemonade frozen slushy that the sell off the carts in DL is milk-free, and there are always things such as the Dole pineapple spears to snack on as well).
I'm sure you guys will make out fine! Have a great trip!
Jennifer