Welcome to the QuickBooks Community, @Capermartin.
Thank you for posting here in the Community.
In QuickBooks Online, there isn't an option to set the closing date for each month. Yes, your right, there's only one field to choose for the closing date. Let's figure it out by following the outlined steps.
Here's how to set a closing date:
2. Under Your Company, click Account and Setting.
3. From the left panel, select Advanced.
4. Choose the pencil icon, from the Accounting section.
5. Select the Close the books checkbox, enter the Closing Date.
6. Choose either Allow changes after viewing a warning or Allow changes after viewing a warning and entering a password from the drop-down list.
7. Enter your closing date Password, then Confirm Password fields.
8. Click Save, once done.
Once completed, you can track changes made of the closing date warning in the Exceptions to Closing Date report.
You can check to this article for more detailed steps about changing the closing date or forgot the password: Edit your Closed Books.
Fill me in if you have other concerns and questions. I am always here to help.