You can do this in a custom theme. Override the head_script() method, get the user level there and output in a JS variable. The function qa_get_logged_in_level() only gives a number so you'll have to compare to the predefined constants like this
public function head_script()
{
parent::head_script();
$levels = array(
QA_USER_LEVEL_BASIC => 'basic',
QA_USER_LEVEL_APPROVED => 'approved',
QA_USER_LEVEL_EXPERT => 'expert',
QA_USER_LEVEL_EDITOR => 'editor',
QA_USER_LEVEL_MODERATOR => 'moderator',
QA_USER_LEVEL_ADMIN => 'admin',
QA_USER_LEVEL_SUPER => 'super',
);
$userlevel = qa_get_logged_in_level();
$levelstring = isset($levels[$userlevel]) ? $levels[$userlevel] : 'unknown';
$this->output_raw('<script>');
$this->output_raw('var q2aLevel = '.qa_js($levelstring));
$this->output_raw('</script>');
}
Hope that helps!