Happy to have you here in the Community, @dhedley. Let me help you with what VAT code to use for your Non-VAT supplier in QuickBooks Online (QBO).
Yes, you can use the No VAT code since your supplier is not registered. This code is for goods and services that are outside the scope of VAT. We'd recommend looking for further information on what VAT codes to use for your sales taxes by checking this article on QBO UK.
You can also refer to this UK Government article for more information on when to use No VAT code.
If the business is fully VAT-registered, kindly follow this article to set up the VAT codes and rates: Set up and edit VAT settings, codes and rates.
If further assistance is needed with what codes to use in setting up VAT, we'd recommend speaking with HMRC. Have a great day!