You can customize you invoice template to show the VAT Number using the Custom Form Style feature in QuickBooks Online (QBO).
Here's how:
Click the Gear icon.
Under Your Company, click Custom Form Styles.
To create a new template, click the New style button in the upper right-hand corner.
Select Invoice.
Go to the Content tab to add the Customer VAT number as Display.
Click Done when finished.
Once you create the invoice, use the template and click the Print or Preview button to see the VAT number. I've attached a sample screenshot for your visual guide: