I applaud you for doing sound at your church. I did that for many years and it can be a thankless job.
That Yamaha mixer changes things somewhat. This is a workable scenario.
You don't take the signal from the QSC's output. You take if from it's input. That's to say the output of the mixer.
You would take the output of the mixer, split it, and send one side right back where it normally goes (The QSC amp?) and the other leg to the "aux" input of that receiver in the other room.
Of course, if we knew exactly what mixer and receiver we were dealing with, perhaps we could be more helpful. You basically asked "How much wire do I need" and left it at that. Make and model number, please.