I don't eat dairy, and when I was there in November I was happily surprised by how easy it was to get soy milk! Really, it's pretty much everywhere (but don't hold me to that, because I am not 100%), as far as I could tell. They had three different flavors at my resort and since I was on the dining plan I just stocked up on them for the morning. I'm 99% sure I saw soy milk in the parks, too. I'm pretty sure though if it's not (and I would be surprised if it wasn't), you could always bring it into the parks with you if your child has an allergy.