As things stand at the moment, copying quizzes from one Moodle course to another is not optimised. You have to include the Question bank in your backup file. If you don’t there will be no quiz in your copy either. The problem is the copying the Question bank is an all-or-nothing affair. Even if you are backing up just one quiz, you have to copy the whole Question bank, including therefore questions that are totally irrelevant and will not be used.
There has been some discussion about this on Moodle forums and wikis. See, particularly, How to minimize the question bank when doing backup/restore. The workaround described on that page will work for any teacher that has access to an empty Moodle course where they can prune the Question bank back to include just the questions that are really needed.
If you don’t do this and you copy quizzes around between classrooms, you’ll find your Question bank grows like a rolling ball of snow, to no purpose at all!