Walt Disney World is very conscientious about dietary concerns and accommodating to special needs.
Juice boxes are readily available in all resort food courts and in most quick service restaurants. Fresh fruit also is available in many places. Every Disney World room is now equipped with a small refrigerator, too, if you need to store juice or other food necessities in your room.
You are welcome to bring juice boxes, water or other non-alcoholic drinks with you into the parks. You also can bring snacks. I suggest you stow them in a backpack or small, easy-to-carry soft cooler.
If you have specific dietary requests, you can ask to speak to the chef in any restaurant to discuss them.
I hope that helps put your mind at ease. Please let me know if I can answer any other questions before your visit. Enjoy!