If the QF flight is scheduled to depart within 24 hours of the time you arrive to check-in at HKG, you should be able to check in online with QF and obtain a BP. If you can do that, CX will have no problem reprinting the BP for you.

There have been problems when my next flight has been scheduled to depart more than 24 hours from the time I checked in, so I couldn't get my own BP, but CX was able to get a BP after about 15 minutes (initially, the agent got it wrong and somehow moved me to the previous day's flight!)

When my subsequent flight has been more than 36 hours away, they couldn't get a BP at all, but they can still check the bags through, since this is a manual process where they just type the flight numbers and dates onto the tag.

To reduce potential problems, you should check with a QF agent at AKL that your bag has been received by them.