Looking at BA, they are looking for H, B or Y fare, earns 20 TP rather than 5 for M/K.

I see an H fare for AU$586 - it appears to be bookable using the American [+] Australia link on the above script.

Note that the OP may wish to consider the AU$1060 'D' fare that earns 40TP's.

Another option is the H fare is available via SYD or BNE for ~AU$600 - earns double the TP's.