You can file the 1st Quarter of 2021 monthly dues next year. Right now, what you can file is the 4th Quarter.
We don't automatically file forms on your behalf. When a form is due, you need to log in to your Intuit online Payroll Enhanced and QuickBooks Online Payroll Enhanced account, and either submit the electronic filing, or view, print, and archive the manual filing.
In general, quarterly tax forms can be filed electronically or manually. You can e-file Form 941 through your Intuit Online Payroll Enhanced and QuickBooks Online Payroll Enhanced account if it's active for federal electronic services.
I've also added this article that can guide you about filing forms in QuickBooks Online: