You need to move the Counter object as well. You can do it at any time after you call QThread::start() but you have to do it from within the main thread
Should I create method in BackThread, that will perform this, and call it from main thread after QThrea::Start is called?

No, you can connect one signal to another signal. This way when one is fired, the other one is emitted as well (we call it signal propagation).
Hmm, I'm little confused now. Could you add this to code I posted, with some explanation?