Can I include Javascript/jQuery in a page?

You need to make sure that jQuery is loaded, so that you can use it.

In functions.php:

function namespace_enqueue_scripts() {
    if ( is_page( 'slug-of-new-page-you-are-creating' ) )
        wp_enqueue_script('jquery');
}
add_action( 'wp_enqueue_scripts', 'namespace_enqueue_scripts' );