You need to specify the post type to be a post – try this for your $args instead:
$args = array(
'post_type' => 'post', // Specifying you want posts only
'posts_per_page' => 1,
'orderby' => 'rand',
'post_status' => 'publish',
);
And most importantly, you need to apply the $args to your query, so do this for the loop:
while ( $the_query->have_posts() ) : $the_query->the_post();
See this in the Codex.