Welcome to the QuickBooks Online community family! Making sure you have every sales tax code needed for your business is our priority. I'll be happy to assist you with this.
After you turn on sales tax in the system, QuickBooks not only automatically creates the GST/HST-QST Payable account to keep track of all sales taxes you collect and pay but also sets up a list of sales tax codes for you, based on the province you selected. To therefore add a new tax code on an invoice that's specific to another province, you'd have to turn on its corresponding tax agency in the sales tax centre. Here's how.
Go to the Taxes menu and select Sales Tax. (Tip: If you use payroll in QuickBooks Online, you may need to select Sales Tax as opposed to Payroll Tax.)
Click on Manage sales tax, then Add tax.
Select Add next to Start tracking in a new province.
Choose the province for your new tax code (in this case, Quebec).
Fill in the required information and then click on Add.
This will automatically set up a new agency for Quebec and the most common codes for that province, such as QST. For more on how to add new sales tax codes in QuickBooks Online, check out this article: How to set up a new sales tax code