If you were issued a single ticket LAX SYD BNE and the baggage allowance was 2 pc on QF, then 2 pieces it would be. United's policy is one bag and pay for the second for general traffic.
A QF fare LAX SYD BNE would carry 2 free pieces up to 23kg each.
If you are however on seperate tickets QF to QF then you will have a seperate allowance on each leg. 2 pieces trans Pacific and 1 piece domestic.You obviously got a staff travel bonus on UA as they normally charge USD 65.00 for the second bag.
A QF ID ticket LAX SYD BNE would have been on the same fare basis, albeit a rebated one and as the fare bases are the same or it is one fare construction unit with combineable fare types then the 2 bag bit would have carried through.
Hope this clarifies a somewhat muddy stream.
Best regards
EWL