Hi Elisabeth,
I have visited Walt Disney World both while I was pregnant and with a toddler, so I know the unique challenges that each of these can pose. The good news is that Walt Disney World is such a guest-friendly place that you will still have a great time!
You are welcome to bring food and drinks into the theme parks, as long as you do not bring in any alcohol or glass containers. We always bring bottled water with us, as well as snacks. Your daughter probably has her favorite snacks, and you should bring those with you. You can also bring a cooler if you like; however, it can be no larger than 24"x15"x18". We have always found it easier just to toss snacks into our backpacks. We also found it a good idea to bring some coloring books, crayons, and stickers with us to entertain our daughter if we wanted to take a little longer at a sit-down restaurant. As to your little one's allergies, you should always mention them at any food service location at Walt Disney World. Disney is wonderful at working to be sure that a guest's allergies are managed and that everyone can eat safely.
When my daughter was a toddler, I found that keeping her on her schedule was key to keeping her happy. She took an afternoon nap, so we always headed back to our resort mid-afternoon. This will also allow you to take a rest! If you find yourself in the park and either you or your daughter need a break, head for the
Baby Care Center.These wonderful centers are located in all four Disney theme parks and provide a place to feed and change your little one, and just get them away from the hustle and bustle of the theme park if you need to.
I would love to help you plan further, however, I am limited in the amount of space that I have to answer. Please do not hesitate to ask if you have any further questions!