Hi, Debbie! Welcome to the Disney Parks Moms Panel. Thank you so much for bringing us your question.
According to the Disney Dining Plan guidelines, children under the age of three "may share from an adult plate at no charge, or a meal may be purchased from the menu." If you choose to have him share from your plate, you will need to be sure your meal is allergy free. If you request a special meal for him, you will pay an additional charge. My Moms Panel sister, Crystal, is an expert at allergy-free dining at Walt Disney World Resort and has some fantastic advice on how to dine allergy-free.
We visited Walt Disney World Resort when my youngest was 15 months old and we were also on the Disney Dining Plan. While my son does not have a food allergy, he was an extremely picky eater and wouldn't have eaten from anyone's plate or off the children's menu. We brought prepackaged ready-to-eat toddler meals that did not require heating as well as snacks for him into the Theme Parks. He would happily eat his food while the rest of us ate our meals. We had no problems with this and it worked out perfectly for us. This may be a great option for your little prince, as I can imagine at 13 months a kids meal would be entirely too much food for him. You can bring these meal options from home or use a grocery delivery service such as gardengrocer.com to have items delivered right to your hotel.
Wishing you and your family a magical vacation, Debbie!
~Rachel