I'm 15, and when I went to WDW, I took an afternoon nap almost everyday. I think at least a rest in the middle of the day is a must because it does get tiring walking all over the place.
Maybe you should think about doing some activities in the morning, then rest, and start back up again in the late afternoon/evening. Since Disney is more busy in the afternoons, perhaps it's a good idea to rest during that time.