If you go through the site upgrade process (of which there are several in between steps), you should keep everything, except any non-supported plugins. The assignment was replaced with a much better version but you will have the ability to upgrade all your assignment instances, also the quiz that also improves greatly.
If as suggested, you build a nice new shiny(!) 3.1 or 3.2 site and import your courses, you will lose all user data.
Some people keep an archived copy of their 1.9 or older sites online so that the data is accessible and then just start a fresh site. This might be another solution for you and would be the easiest overall.