If you only have a few courses, then this would be an easy to achieve that. You will just start from scratch and make sure that you call your new moodledata folder something different, create a new database and install where you want. Then export the course with user data and import into the new moodle.
Alternatively, you can move the folder and change the location in config.php. If your site has a dns name, then you should be ok with the links as they are not changing, just the location of the folder is changing.
On a side note, if you are planning to move outside of your html folder, with most hosts, this will block access to the site.