The FAQ on copying data to/from an offline testing server, usually a PC, covers the same process, but instructs to use FTP to copy the files, since that's what most people have available to them. Most don't have SSH access let alone the knowledge to use command-line instructions on a Linux server.

Basically the process is this:

1. Clone the files. Since you're working on the same server and same hosting account, AND you have shell access to your server, using your command-line "cp" approach is fine.
2. Edit the cloned configure.php files to contain the correct database details for your testing database.
3. Use phpMyAdmin to export your live database using the FAQ instructions.
4. Use phpMyAdmin to restore your database backup into the database used for your testing site.

5. Since you're running on the same server and hosting account, it's unlikely that you'll need to use fix_cache_key.php on your site.