Hi there Mychelle,
As a nursing mama, The Walt Disney World Resort Baby Care Centers, (found in each park), are going to quickly become your best friend. The Baby Care Centers are like an oasis of Peace and air conditioned relaxation when you need it the most. Inside, you'll be able to sit down in a quiet room to nurse your little one and let her nap for a while to beat the heat. These Baby Care Centers are also filled with all sorts of baby necessities too. There is even an area protected by privacy curtain if you are more comfortable pumping there.
Unfortunately, the rooms at Disney's Pop Century Resort, although equipped with a mini-fridge, do not have freezers in them. The only thing I can think of would be to pack the pumped milk in a double baggie of ice and store in the refrigerator... not 100% sure of the storage guidelines, even though I also nursed my daughter. Another option would be to consider switching to a resort that offered a full kitchen... Maybe a DVC Villa or a cabin at
Fort Wilderness Resort and Campground.
Also, Amazon does sell a portable freezer, which may be a convenient purchase for you. You can have this shipped directly to your resort and this would be more economical than switching to a "full kitchen" room.
Hope this helps, Mychelle and Best Wishes,
Amanda F.