I would expect they should offer you something although I suspect it's most likely going to be vouchers which will need to be spent on QF flights or duty free.

Do remember before leaving the baggage services desk that you should always ask for cash or form to allow you to claim back emergency clothes etc from the airline.

In your case it actually sounds like QF messed up once and BA then messed up too when transferring your luggage onto your CAI bound BA service. With that in mind, I suspect you will have to contact BA re the CAI baggage and QF for the Australia/NZ baggage issue. BA will probably offer compensation similar to QF although generally airlines like receipts.

I do hope you had travel insurance as this should cover you in just these types of situations. I had a recent trip on LX where my luggage missed my transfer and my insurance allowed me to purchase emergency clothes etc which made life much better.