how to create custom category

apology for this rookie question, i managed to create my own index.php and single.php templates.

I wanted to create a category page that displays 10 posts inside animals category with pagination.

code below goes to my category.php

<?php get_header(); ?>

<div id="container">
<div id="content">

<?php $my_first_category_query = new WP_Query('category_name=my_first_category'); ?>

<?php while ($my_first_category_query->have_posts()) : $my_first_category_query->the_post(); ?>
  <!-- Do special_cat stuff... -->
<?php endwhile; ?>

		</div><!-- #content -->
		</div><!-- #container -->

<?php get_footer(); ?>

after, should i just go localhost/site/category.php?
ill appreciate for any assistance ??
thanks