Quick press publish post hook

As Wyck said, it’s just a form that uses post.php. To check if QuickPress is the one making the call use:

add_action( 'publish_post', 'check_for_quickpress_wpse_109961' ); 

function check_for_quickpress_wpse_109961( $post_id ) 
{
    if( 'post-quickpress-publish' == $_POST['action'] )
    {
        // do_something();
    }
}