Disney has said they can accommodate special requests with advance notice. Do you have a few days between checking in and your HDDR reservation? Then I would check with your concierge at your hotel for help with that. If it's your first or second day, then call Disney and ask to speak with the chef at the Hoop Dee Doo directly, about 3 days or so before you go. They should be able to accommodate whatever you need regarding allergies, and/or vegetarian.
Good luck - let us know how it goes!