***<IF money was not a consideration, ie, you would be happy to go premium cabin, then read my as some would say, (rubbish).>
If I had the $ again, I would do the EK F flight CHC - SYD, as it will earn 120 QF SC and then 40 QF SC for the J from SYD to MEL.
I have done the F on EK and the J on the QF 737, F wins hands down, just for the bar experience on board the 380.
If you can't afford F on the EK, then J on the EK would be a great consideration over the J on the QF 737.
If you really must, then that 737 in J from CHC at about 13.30/14.00 to get to MEL about 4pm or a bit later, would be the one that gives the most time in CHC daytime departure direct to MEL.
SYD Airport Rydges quite good too, or the Ibis Budget if you have to.
Because the EK flight from CHC comes in at 18.30, and you have to do incoming immi in SYD, I would over night in SYD and get the first flight next day back to MEL, ideally you could get the last QF flight SYD - MEL, but I would do the next day's one.