It depends on the type of payroll subscription you have.
If you're using QuickBooks Online Payroll Full Service, Intuit will pay your taxes and will file your tax forms. If you're using QuickBooks Online Payroll Enhanced, you will need to pay the taxes either by check of e-pay.
You can go to the Account and Settings section to verify which subscription you're using. Here's how:
Click the Gear icon and select Account and Settings.
Go to the Billing and Subscription tab.
Go to the Payroll section.
Let me know if you have other questions. I'd be glad to help you again.