Laan's steps..

First of all, you can not do this just in Adobe AIR. So, a third-party tool is a good choice:

1. Install 3rd party hotkey application (like AutoHotkey or HotKeyBind)
2. Configure hotkey application  to launch your AIR application.
3. In your AIR application, register for the NativeApplication.invoke event, and watch for arguments to do something.

Maybe the Adobe AIR will add those features in the future.