I think going out via MEL and returning via SYD are all a good measure.
MEL airport T1 to T2 is just a few mins walk, and as QF would most likely have swiped your passport in CBR and issued you a whole trip of Aust BP, you don't have to approach QF in MEL, just go straight from getting off plane at T1, walk to the auto gate prior to security screening at T2, scan your BP onto the reader, and the swing gate will open for you, here you might be picked for a bomb residue wand test in group of 5, or go straight to outgoing passport control, then int security screening, then to the duty free area.
Coming back via SYD, you would have more chances of getting home to CBR, even with the 717 or the Dash8.
If you come in from DXB during the day, there are a lot of planes to take you back to CBR, small or large!
Don't worry, what you are about to do, a lot of us on here have done it many times.
Since 2013, I must have done at least 10/15 ADL - MEL/SYD/BNE trips to NZ, have made QFF SG 3 years in a row!
No QF flights direct from ADL internationally now, so have go through eastern states to get any where world wide.
Coming back, T1 SYD to T3, the QF seamless transfer bus can be a sardine can, stuffed full, try to have HLO only if you can.
Good chance to look out the bus windows at aeroplanes, very close look, if you are an av geek.
Closer than any other airport in the world, as the bus travels on the inner secure road, very close to the rear of planes parked at the int terminal and also the cargo area, before the swing around to the bottom of gate 15.
DXB might or might not issue the BP SYD - CBR, but the T1 staff at SYD int should be able to issue one to you, if DXB EK staff don't.
Edit: for incoming into SYD T1, all bags will have to be physically taken off the carousels by the traveller, even if through tagged, and you will have to pass incoming customs and quarantine checks, most of the time, they don't pull people aside, if you travel is one of the norms.
OffT
On my trip out to NZ and back into MEL, out via SYD 29/12 Dec, and returning via MEL 01/01/23, no one asked to see my tripled vaxxed cert, I was carrying my own blood pressure meds, with cert, on coming into MEL T1 int, the ABF guy looked at my IPD (incoming pax declaration), and mentioned casually, you travel very light, (I thought oh poo), but when he saw it was NZ, and I said I travel light, he just took the small printed self processing slip and IPD and that was it, I was clear.
Don't bring back food, don't bring back alcohol, don't bring back duty free, be honest on the IPD, and the incoming process can be easy.
Granted that if a person came in from China/Vietnam with 1 huge trolley load of items, they might want to check the contents of the bags.
OnT.
For MEL, QF1527 arr 19:15
EK407 dep 22:00
2.75 or 2hrs45mins, for MEL is enough time, on the same PNR.
For SYD, hope your EK is the one arr at 07:00, and not the 22.30.