Not sure which state taxes you are talking about, but QB will not do them
The available liability period can only extend back for a year. If you archive the form from these periods (2015, 2016, and 2017), you'll need to contact Payroll Support.
They can help you get it unarchived.
You can also use the Payroll Tax and Wage Summary Report to get the details and file it manually.
If you have further concerns, please don't hesitate to reach out. We're here to help.