You need to contact Disney's special dietary team. They are outstanding on an unrivaled level with dealing with special dietary needs and severe, even life threatening allergies. If you send them an email detailing your DD's specific allergies they will email you a list of attachments explaining what is safe and what is not. For TS meals they will also note it on your ADR if you have one and the chef will come to the table to discuss your requirements. No food will be permitted to be brought to your table prior to this. They are very good.
I will get you the email address.
It is also worth a visit on the DISabilities Board where there are numerous threads and reviews on dining with allergies.