I'm not sure that you can do this. A project in QC is supposed to be a self-contained entity, that is, there is no way (that I know of) that you can automatically move data between projects.
Sure, you can copy and paste data, as well as create a project with another one as base, but that is probably not what you want.
I would rather have manual testing and automation in the same project, which makes more sense I think. The point is that the project is supposed to identify the test object, rather than the test methodology - the latter can be done better in Test Plan where you specify a Test Type when you create your test.
This way, you will have all defects and test reports for your test object in the same project which will make it all the easier to track what is going on.