Thanks for your posting! There are two common approaches to integrate automated tests with TestRail and TestRail's API.
The first one would be to record and submit test results as your test automation tool goes through the tests and this is often implemented by integrating directly with the test execution engine (via listeners, for example). This often requires a tight integration with the test automation tool and using the tools & script the test automation tool provides (VBScript in your case, for example).
The other option is to use result files most test automation tools generate and this can be implemented as a post-processing step and independently of the test automation tool. This is usually the easier and most flexible option and the one we also recommend most of the time. The advantage of this option is that you can use any tool or programming language (such as Python) and independently of running the actual tests. QTP seems to have support for result files as well via the Export/Save File features after running your tests.
I hope this helps!