If it were me, I would be assuming business class checking was ok. You are checking in for the BA J flight at the MEL counter, so should be entitled to the J checkin desk.

I would certainly go to the desk and hand over your J ticket and plead ignorance if they stay you shouldn't be in that line. But I doubt any QF agent would turn you away to the Y line in this situation.

QF domestic lounge access is a different matter, and the MEL lounge domestic lounge is not known for its flexibility. If the J flight was on the same ticket you may be able to get access, but otherwise only the appropriate level of membership will get you in.