Welcome to disABILITIES.
There are Companion Restrooms in each park that do have changing tables, but my best guess is that most of them are only about 4 feet long and are a little too high to change an adult (close to waist height for me and I am 5 foot 7).
There is a very nice First Aid station in each park that will suit your needs. They have individual cubicles that can be closed off with privacy curtains. There is a sturdy cot, a small table and chair in each cubicle. I've never counted the number of cubicles in each one, but there are enought that we've always had our choice of several empty ones. There is also a wheelchair accessible restroom in each First Aid (you could wash hands there, but there's no cot in the restroom). We have used First Aid in all the parks to use the restroom or to rest after a seizure and have found the staff to be very professional and nice. It's also a good place if your DD needs to lie down to rest or stretch. The area is kept quiet and dim, so it's very calming.
First Aid is well marked on the park maps, but here's where to look:
MK: Just off Main Street between Casey's Corner (a hot dog restaurant on Main St. and Crystal Palace.
Epcot: In front of the Odyssey Center (on a walkway that goes between Test Track and World Showcase)
AK: Next to Flame Tree Barbecue on the side toward Africa
Studio: Just to the left as you come into the park, next to Sid Cahuenga's One-of-a-Kind shop