Welcome to the QuickBooks Community, @cchristison.
Let me help you set up Taxe de vente du Québec for your purchases. For English versions of QuickBooks Canada, TVQ is displayed as QST. To start tracking this tax in QBO, you'll need to set it up in the Sales Tax page.
Go to the Taxes menu, then Sales Tax.
Choose Manage Sales Tax.
Select Add tax.
Press the Add option in the Start tracking in a new province section.
Choose Quebec, then fill out the tax details.
Once done, press Add. The system will automatically input the rate for QST.
Review everything before clicking Done.
Now, when you purchase something, just assign the QST in the Sales Tax column. See this:
Here are the links on how to set up and manage sales tax in QBO Canada (English and French):
Come back here for updates or additional questions about setting up sales tax in QBO. Also, let me know if this is the option you want to do or if there's anything else you want to record in QuickBooks. I'll be right here to help.