Not really getting the post types

Trying to get some understanding regarding the post types.
In this case I’m working on my own theme and in index.php i have this code:

global $post;
dx($post);
dx(get_post_type());

(the dx function is just a small function that makes this:
function dx($a) { echo '<pre>'; var_dump($a); echo '</pre>';})

Now, to the problem. In a plugin i register e new post type, let’s say ‘cars’. something like this:

add_action( 'init', 'create_cars_post_type' );
function create_cars_post_type() {
  register_post_type( 'cars',array(
      		'labels' => array(
        	'name' => __( 'Cars' ),
        	'singular_name' => __( 'Car' ),
        	'slug' => __('cars'),
       		'view_item' => __('show cars')
      	),
    	'public' => true,
      	'has_archive' => true,
      	'hierarchical' => false,
      	'rewrite' => array('slug'=>'cars')
    )
  );
}

The question regards the rewrite part. Lets say I create a nice car, let’s call it “volvo”. Now the url is nice and is [mydomain]/cars/volvo.
However, my code from index.php gives me this:

null
boolean false

Ok, it’s no post and the post type can’t be found.
If i set the rewrite to false my index.php outputs the post object and my post type -> but the url is now [mydomain]?cars=volvo and that sucks. 🙂

What am i missing? How can I have nice URL:s and make WP accept it as a post?