This quiz had been online, and you just changed categories? Then, yes, you can submit a new quiz at the same time.
You will have noticed that the quiz was automatically pulled offline when you tried to change the category. This is to prevent authors moving quizzes around willy nilly, and making nonsense of the categorization system. It doesn't hurt to talk over a category change with an editor, and then ask the editor to make the change. Saves taking the quiz offline, and ensures that your quiz will end up in the right spot.