Welcome aboard, Nadia! Rest assured that Disney Cruise Line is excellent in assisting guests with all sorts of food allergies. I'm glad you've already noted your daughter's allergies on your reservation. Your servers will receive that information to help them better prepare and offer you options.
As you board the ship, guests can head to Cabanas (until 3:00) or Enchanted Garden for lunch. I suggest that you choose
Enchanted Garden which is usually open until 2:00 on embarkation day. I say this because Disney Cruise Line recommends that all guests with food allergies try to eat most often in the main dining restaurants. The galleys there, as well as the service team, are very well equipped to handle allergies and their larger galley size prevents cross-contamination of allergens much easier. You are able to eat breakfast, lunch and dinner in the main dining restaurants, should you choose, however you are of course welcome to enjoy the buffet at Cabanas and the quick service spots should you feel comfortable. In Enchanted Garden on your first day for lunch, you can chat with the server and head server about your daughter's allergies and they'll be happy to provide you with suitable options, as will your servers each night at dinner.
Disney does not allow most food items to be taken off the ship due to customs regulations. You'll want to plan to purchase lunch in port or head back to the ship for lunch. However, if you pack some pre-packaged dry snacks you are welcome to take those with you into port.
I hope those details help ease your fears of cruising with allergies, Nadia. Disney takes this very seriously and will work with you to ensure your daughter, just like everyone else onboard, has a very magical experience! Happy planning! Please let me know if I can answer any other questions before you set sail!