My six year old has been to Disney once per year and I LOVE MY STROLLERS! Used a Sit & Stand for several years and then started renting the doubles from Disney. His older brother often rides with him, they don't become too tired too fast, they have their own "haven" out of the sun, and they have fun sharing private jokes, etc... My husband and I have conversations as we walk (w/o constant interruptions), and we always have somewhere to place our bags, prop snacks, and so forth.
Are my children old enough to walk? Yes, and they do walk--but, when they get tired, they have somewhere to rest. It's everyone's vacation and we are all happier if the children are having fun, their legs don't hurt, and they don't keep begging to go back to the room.
Now that double strollers are SOOOO expensive at Disney, we don't know what to do for our upcoming June trip.
My advice is to at least bring the stroller to Disney --you will have it if you decide to use it.