I had to exclusively pump for my daughter too, as she could not nurse (no suck reflex when born, would latch but could not drain milk efficiently due to her poor suck). We went to WDW when she was 8 months old, and I was still EPing. I wrote 2 advice posts on EPing at WDW..here are the links:
My experience EPing at WDW
My top tips for EPing at WDW
If at all possible, I would highly recommend getting an Ameda Purely Yours pump - whether renting one just for the trip (some hospitals may rent), or buying one. It runs on batteries, so you don't have to have a wall outlet. It was *invaluable*.
I started out pumping and keeping milk cool in a cooler, and bringing it in the park with us (the stroller company we rented from gave us a cooler with the rental, we just put that in the bottom of the stroller) - but DD never did like cold milk (still doesn't) and we found it very difficult to warm up the milk as we needed it.
Breast Milk is good at Warm Temps (80-90 degrees) for 3-4 hours . What I ended up doing was using cold milk to heat up her first bottle of the day at the hotel (where we used a coffee maker to heat up water to warm her bottle), but then once in the parks I would just feed her whatever I last pumped. I didn't have a great supply so I had to pump 7-8 times/day, so it worked out that DD would drink whatever I last pumped when we stopped for the next pump session. It was never more than 3-4 hours between pumping sessions.
I did update my tips thread with the Tommee Tippee Bottle Warmer thermos link - if you need to use cold milk, this is a GREAT way to keep hot water with you all day long (and it comes with a cover that you can put the water/bottle in to warm). It keeps the water hot all day long.
Aside from the ease of pumping with the batteries - the freedom of location that the Ameda gave me really helped me feel like I was not missing as much of the trip. My nephews were with us as well, and if I'd had to go to the Baby Care Centers all the time to pump, I would have missed out on so much. With a nursing cover, I pumped all over the place (in as out of the way/unnoticeable places as possible) - but not being tied to an outlet *really* helped. Because of this,t hough, I didn't spend much time in the baby care centers so I can't really speak to what they are like or how pump friendly they are.
If you have any questions at all about EPing through WDW, let me know! EPing is hard, and at Disney it can be even harder! I'd love to do anything I can to help another mom have a good trip