The Fastway Ireland shipping calculation is performed on the Checkout Page only.
As Ireland does not have any Post Codes, you will need to disable the Post Code field on your WooCommerce Checkout Page.
This can be achieved using this extension. https://wordpress.org/plugins/checkout-manager-for-woocommerce/
The Fastway rate will be calculated using the Country [Republic of Ireland] and City fields [example:Wexford] on the checkout page, if you do not disable the Post Code field your customers will not be able to check out/ finish the transaction as this is a required field in WooCommerce.