I put some code up that starts a thread that does this. It is windows specific, but it does the job.
Clipboard Shortcut/Hotkey binding with Qt outside of application
One alternative to all of this, is to go to a shortcut to your program, go to its Properties, and then click on the shortcut area and type your desired shortcut. As long as it doesn't overlap with existing hotkeys that are registered in windows, it should work, without a hidden presence of your app in the system tray or some other background thread.
Hope that helps.