Have Disney add the request for it to your reservation. You can also request it once you are there (they also have Diaper Genies for you to use!) Your stateroom host will be happy to bring these for you and set them up.
Since they have limits to the numbers of children they will allow, I'm sure they have enough pack n plays for all of the children under three that would be on board.
I think I would go through the trouble of bringing my own. Babies get sick so easy, and that is a great way to spread germs. If they are as "clean" as the strollers that I have seen them loan out, no thanks.
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