Filtering post-formats from the loop using new WP-Query();

You should be able to exclude posts with a specific format using WP_Query’s tax_query parameter.

Eg.

$q_args = array( 
    'posts_per_page' => 1, 
    'tax_query' => array(
        array(
            'taxonomy' => 'post_format',
            'field' => 'slug',
            'terms' => array( 'post-format-link' ),
            'operator' => 'NOT IN'
        )
    )
);
$featured->query( $q_args );

Untested, but should do the trick..