Hello there, qtdds219.
Let me help with your payroll taxes.
QuickBooks Online won't be able to calculate taxes if you won't process a payroll. However, you may need to file a zero return which depends on the requirements for your state. You may check with your state what are the things that need to be processed. You can also visit our Payroll Tax Compliance Links page for additional details.
In addition, the IRS doesn't require you to file Form 941 for the quarters that have zero tax liability. Though, you must notify the IRS not to expect four Forms 941 from you throughout the year. This is applicable especially to those seasonal employers. When you file Form 941, you have to check the box on line 18 to every quarter you file the said form.
You may visit this page from IRS about Instructions for Form 941 (01/2020). Also, if the reason why you did not process payroll is because of closing your business, you still need to file your quarterly forms for both federal and state, then notify them about the closure of the company. Please check this article to learn more: Close business and finish payroll tasks.
Please post again if you have more clarifications. Take care always!