What argument does my function need to echo get_results() query results

Why don’t you just do..

add_action( 'wp_head', 'quick_qs_db_css', 100 );
function quick_qs_db_css() { ?>
    global $wpdb;
    $table_name = $wpdb->prefix . 'qs_css';
    $db_css = $wpdb->get_results( 
        "
        SELECT qs_the_css 
        FROM $table_name
        WHERE qs_css_id = 1 
        "
    );
    <style type="text/css" id="db-css">
    <?php echo $db_css[0]->qs_the_css; //outputs null ?>
    </style>

<?php }

Seeing as you are using it everytime head is loaded, it would make more sense than to keep the two separate unless there’s good reason for it?