We have always rented cribs, from A Baby's Best Friend in Orlando.
They offer a gazillion baby items for rent, and they drop it off for you, and pick it up from the hotel. We've done it I'd say at least 5 times? Maybe 6?
They are super easy and professional, exactly what you need when traveling with little ones.
I think Disney only offers the pack n plays- so you may want to call and ask.
Good luck!