Our daughter has multiple serious, anaphylactic-causing food allergies (Peanuts, tree nuts, sesame, coconut, shellfish and seeds).
We have been on two Disney cruises with her and had a wonderful time on each cruise.
After you make your reservations, make sure that you note that your daughter has food allergies. There is a form that you have to fill out and return to guest services.
When you check into the MDR restaurant the first night, mention that your daughter has food allergies.
My daughter was assigned someone to check with her everyday to help her order her food for the next day. That was the only pain point - with her having so many allergies, she couldn't eat just anywhere - we had to plan ahead.
We ate dinner in the MDRs and they always had whatever she ordered ready for her at dinner.
If we wanted to go to Cabanas, we had to meet with the manager at the buffet who would take DD around the buffet to find safe food for her to eat.
We found that Disney took her food allergies seriously and helped us to have a safe, enjoyable time on our trip.
Please note, however, that the excursions can not guarantee safe food away from the ship. We brought packaged items that were safe for her with us, so that she had something to eat on our excursions.
We also found that the MDRs were also able to make her something "off the menu" in order to accommodate her food allergies.
That has been our experience. It made for two very enjoyable cruises. We wouldn't hesitate to go on another
Disney cruise!
Good luck!