What we do is add the academic year to the shortname and idnumber e.g. ABC101_15, ABC101_16
When you create the new course, you can use Moodle's Import facility to copy over all the content. This will effectively create a new copy of the quiz, in your case, and drop all the user data from the previous year.
Your teachers will have access to this import process so this is something they can do themselves.
You then need to ensure everyone's enrolled correctly on the year marked courses - which may need changing whatever processes you use.
To help organise your course on the My page, we use the Filtered Course List block.
Hope that helps.