If you are not VAT registered, please do not turn on the VAT center. So that QuickBooks will not calculate and submit VAT to HMRC. However, if you already turned it on, the only way you can proceed is to use the NO VAT tax code.
You can read this article as your reference for NO VAT tax code: Common VAT Codes.
You may also use this article that helps you keep accurate records of your tax that you collect and pay: VAT: Getting Started.
If you have additional questions, feel free to leave a message in the comment section. I'll be happier to help. Take care, and have a great day.