Don't forget EK. I'd probably do a visit to tokyo once instead unless you have more of a reason to do so such as family or events to see.

SYD-DXB (possible 3 days stop) EK or QF
DXB-MXP (your vacation) EK
MIL-TYO (many routes possible) EK, BA, CX, JL, FN
NRT-SYD (QF/JL)