Thanks for checking in with us, Stare.
The option to generate a report to confirm if a job has or has not been invoiced is unavailable in QuickBooks Desktop.
As a way around, you can pull up the Transaction List by Customer report and check the job names from there are already been invoiced or not. See the sample screenshot below.
While this report isn't available, you can submit your feedback to make the program better by going to the Send Feedback Online on your QuickBooks Desktop.
I recommend customizing the report to get the specific details you need. You can also memorize it to save its current customization settings. It serves as your record and helps you quickly access it for future use.
Don't hesitate to let me know if I can be of additional assistance. I'm always here to keep helping. Have a good one!