There are only two ways to nonrev on JQ.
1. have an agreement with QF that includes JQ operated flights or
2. find a compassionate JQ/QF agent who's willing to accept your ZED ticket

Either way, your pass office shouldn't ticket a QF markted flight operated by JQ unless you have an agreement that includes them. Of course, several of their flights operate in markets also served by QF online and/or Qantas Link.