It is my understanding that QF's policy for through-checking bags for different bookings is that they will only do it if the connection is to another OneWorld airline or JQ in some circumstances (int transfer for example).
Of course this does not mean that the policy is always rigidly enforced and you may find a check-in agent willing to through-check bags.
Just because the airline may have an interline agreement with another does not mean they have any responsibility to through-check bags when purchased on separate tickets. The baggage interline agreements normally only apply when the ticket itself is purchased as part of an interline ticketing agreement.
Most staff at WLG are in fact NZ and they will not have the authority to interline the bags.
If they talk to the QF station manager, she will not allow it. She is a stickler for the rules and always has been.
Get the visas sorted and try to delay the trip, which I doubt as they appear to have purchased the cheapest tickets.