I had this same issue on a remote host and what I did was rename my old public_html folder "old_public_html" then name my moodle folder "public_html". Then I moved the new public_html folder to the root so that moodle launched using http://mydomain.com instead of http://mydomain.com/moodle.
The only other change is in the config.php file where the following information will have to reflect your new location:
$CFG->wwwroot = 'http://mydomain.com' ;
$CFG->dirroot = '/home/acctname/public_html' ;
$CFG->dataroot = '/home/acctname/public_html/uploaddata' ;