We have had great success with Keen's for my kids when they were that age and even younger. They will each be wearing them for most of our trip in August (as will my wife and I). They are good hiking sandals with covered toes to protect against stubs. They are also waterproof which is great for Splash Mountain, Kali River Rapids, etc. They can be a little pricey, but I truly believe they are worth it.
Good luck.