It's very much like duplicating your site and you can do the same thing to create the new site. Backup your current Zen Cart folders, files and database and restore them to the new location. Then it would just be a matter of changing some of the info in the admin and editing the configure files to point to the new database and reflect the new domain.

If you have separate databases, changes to one will NOT effect the other, so you don't have to worry about that issue.