Is it possible, when entering an invoice, to show which employee wrote that invoice? And then be able to generate a report containing just those invoices?

I know a way how you can track invoices written by each employee in QuickBooks Online (QBO), steve. 

You can run an Audit Log report to show invoices written by each employee in QuickBooks Online. This report records all account activity in the audit log, such as user sign-ins, changes to settings, edits to customers, vendors, employee

If you assign an employee, you have the option to filter by User, and in the Events section, choose All transactions. Here's how:

1. Go to Reports from the left menu. 
2. In the Find report by name type in Audit Log.
3. In the User dropdown, pick the users.
4. Choose the  Date Changed dropdown.
5. Select All transactions in the Events dropdown.

On the other hand, here's a report you can run to get an overview of the transactions recorded in the system.

Let me know if you need additional information about handling journal entries in QuickBooks. I'll be right here to help you.