Hi there, David.
As a mom to a vegetarian, I always have a line on where I can find things like soy milk. You'll be happy to know that at the resort hotels, in the refrigerators in the food court, you can almost always find individual containers of soy milk, and there will also be regular milk products (whole, reduced fat, chocolate, and skim).
The gift shops will also have various milk choices available. Sizes may vary, but you can usually find whole, reduced fat, skim, chocolate, and soy. I can almost always get a quart or half gallon of regular milk. This view of the
Beach Club Marketplace will show you what many of the grab 'n' go sections of the resort gift shops looks like and where you'll find the milk.
If you don't see the soy milk right away, just ask one of the helpful cast members. They can help you find it or get some for you.
Have a great visit to Walt Disney World, David!