Hi Lukes_mum,
QuickBooks Desktop makes it easy to keep track of billed and unbilled time with the reports that pull from the time tracking feature. I've pulled one you can try that I think will give you the information you're looking for based off what you've said in your post. Pull up the Billed/Unbilled Hours by Person report in the Report Centre. Follow these quick steps.
- Click Reports in the top menu bar.
- Choose Reports Centre.
- Use the search bar to find the Billed/Unbilled Hours by Person report.
- Click the green arrow icon to run the report.
Use the Customize Report button to filter the results you're seeing. The report shows you a breakdown of billed, unbilled, and not billable hours, as well as the date or date range you've run the report for. Check out my screenshot below to see an example of how billed and not billed hours will appear on the report.

I hope that helps give you a better idea of what kind of report you can run for this situation. Check out the other unbilled reports available in the Reports Centre. Let me know if you have more questions!