I suppose you could call it anything you want to. Just don't confuse the client. You could call it: "Benefits of Automated Testing" and list all of the pluses for automated testing, or "Automated Testing Scope Document" and describe what you can and can't test with automation, or even; "Why your testing will cost more than with other providers" and explain that automation requires skilled developers and not just the normal manual testers.
Automation is Programming!
Success is the ability to go from one failure to another with no loss of enthusiasm.
~ Winston Churchill ~
To me a POC or proof of concept is when I automate selective manual test cases with the automated tool, showing the client. Sometimes these can last a few hours to a week depending on their needs.
When you say you already have a tool and a project, and you want to propose automating this project? Are you proposing using the same tool you already have purchased?
If so and you want to show the benefits I would scope out the project as I would any other project prior to starting it.
I would get all the requirements, use cases, and any other documents you have, and determine the time frame, what can be tested (automated), what can not be tested.
Remember though that there are two possibilities here. You can write on the behalf of the tester WANTING To automate, or you can be realistic. What if your findings don't support automation?
So make sure the ROI is there for the company before you hand in an Automated Test plan or proposal. If the ROI is not there and you can't back up the benefits, then you've probably wasted your time and theirs, so just do your homework!