You didn't mentioned what if any status you have with either airline. My understanding is that baggage allowance is generally taken from the first operating airline on your itinerary. So if no status, I would expect, as per QF rules, that you can have any number of pieces up to a max of 23kg in total. See here link.

I can understand your confusion tho, the BA site, here says that the most generous will apply, but then says the number of pieces must conform to BA standard. Surely an oxymoron? To be honest, at CHC I would expect QF to check your bags all the way to LHR, and issue BPs for the entire journey, so I wouldn't expect you to ever face BA about it.