Simply use the backup/restore method.
- Be sure the catalog is clean (reconnect, repair, optimize...)
- backup from the Organizer menu to an external media (USB external drive for instance)
- Install Elements on the new computer
- Do a restore to a custom location. That means you create a new folder and when you do the restore, you state that folder in the destination path.
All files will be restored and if necessary, the catalog will be converted to the new Elements version format.