Try this:

    $args = array(
        'name'=>'header-images',
        'posts_per_page' => 4,  
        'orderby' => 'rand'
    );

i.e. use `posts_per_page` instead of `numberposts` if you want to use `query_posts()` according to the the Codex page:

http://codex.wordpress.org/Function_Reference/query_posts

**Edit:**

Here is one idea - fetch the gallery shortcode ids from a page content with a given slug:

    /*
    * Get an array of the 'ids' parameter from the gallery shortcode that is placed in the content of a post/page with a given slug. 
    * @param string $slug Post slug.  
    * @param string $type Post type.  
    * @return array Array of the gallery shortcode ids parameter.
    */
    function get_gallery_ids_wpse_87978($slug,$type){
    		$output=array();
    		$my_query = new WP_Query(array('name'=>$slug,'post_type'=>$type));
            while ($my_query->have_posts()) : $my_query->the_post(); 
    			$content=get_the_content();
    			preg_match('/ids=\"([0-9,]+)\"/i', $content, $matches);
    			if(isset($matches[1])){
    				$output = explode(",",$matches[1]); // let's take the last set of ids
    			}			
    		endwhile;
    		return $output;
    }		


Usage example:

We have for example a page with the slug `my-gallery-demo` and in the content there is this shortcode like this one:

    [gallery ids="1376,1375,341,213,211,210,209,208,206,205"]

To display `4` random images from this shortcode we do the following:

    // initial values:
    $slug='my-gallery-demo'; // EDIT post/page slug that contains the gallery shortcode 
    $type='page'; // EDIT post slug that contains the gallery shortcode 
    $size='thumb'; // EDIT image size (thumb,large,full,...)
    $n=4; // EDIT number of random images to show
    
    // fetch all ids from the gallery shortcode:
    $ids=get_gallery_ids_wpse_87978($slug,$type);
    
    // get n random keys from the $ids array:
    $random_ids=array_rand($ids,$n);
    
    // display a list of n random images:
    echo '<ul>';
    foreach($random_ids as $random_id){
    	  echo '<li>';
          echo wp_get_attachment_image( $ids[$random_id], $size );
    	  echo '</li>';
     }
    echo '</ul>';