Hey,
When you've created your customer, make sure you include their country in their customer account details.
Providing you've got VAT turned on, when you click on a transaction for this customer- say an invoice, you'll be able to select a VAT Code, when doing this, there's an option for "Manage Rates" within the select code drop down. In this Manage Rates option, you'll find the ability to turn on and off codes as required.
On QuickBooks, you can attribute a default VAT code to a product, service or account - but not a customer.