Hello, Debbie!
Not to worry! My first trip EVER to Walt Disney World was while nursing our five-month old; you'll be so pleased to find that each of the four major parks has a
Baby Care Center, which includes a room for nursing moms only. You'll find relaxing rocking chairs, dimmed lighting and lovely paintings on the wall, a perfect place to sit down in a clean, private environment and nurse your baby. You'll find baby food available for purchase there, too, as well as
microwaves for heating items and highchairs, too. Put a few baby snack
items into your diaper bag and a couple of teethers / toys and your
meals should work just fine.
You'll also find helpful information about
traveling with little ones in this In-Depth Planning page, so be sure to read through that as well. I also really enjoy reading through articles and reviews posted on the unofficial site allears.net. Just put "baby care centers" into the search bar and you'll find lots of helpful information throughout the site.
Hope this helps! Send more questions as you think of them...we love to help!