Hi Heidi,
Love that you are starting your son on the path of a Disney fan early! We have traveled there with our boys since they were infants and have always found it an easy vacation even with small children.
While I have never seen an option for a baby plate of steamed veggies, a number of Disney restaurants do offer a great selection of appetizers and even side dishes which may be the right portion size for your son. The buffet restaurants also have a large variety of salads, vegetables and meats that he may enjoy. We carried finger food snacks, like cheerios and small cans of stage three baby food, with us. Most of the time the boys would share with me. You can find copies of the restaraunt menus at
www.allears.net under the dining option and this might help you decide on your dining choices. You can also ask for suggestions from your server. Often the kitchen can help make a variation of a menu item that would work for him or possibly put together a small vegetable plate.
Another option, if needed is to purchase baby/toddler food while on property. There is a small selection sold at the baby Care Center at each of the parks as well as the sundry shops at the resorts. You can also arrange to have groceries delivered to your resort at check-in. Our favorite is
www.gardengrocer.com.
Wishing you a wonderful vacation!