This functionality is included on the product page and can be enabled in:
WooCommerce => Settings => Catalog => Catalog Options => Redirect to cart after adding a product to the cart (on single product pages)
But to accomplish this on the category page would more than likely require modifying the filter/hook within WooCommerce. Or customizing the content-product_cat.php file and it’s related files.
Take a look at http://wcdocs.woothemes.com/codex/template-structure/ for the guide to customizing the theme/pages.