I'm not sure if there's anywhere on disney to get fresh vege juice, but I;ll bet you could get some at Goodings which is the 24 hour gourmet supermarket in lake buena vista\just take hotel plaza boulevard to end (535) and it's across the street. Very easy to find and very very close!
They have an incredible juice station at FRESH at the Dolphin, and their breakfast buffet is fantastic - just thinking about the made-to-order omelettes, pumpkin pancakes, and strawberry-cream cheese french toast is making me drool!! Aww, now I need a snack!!