You would most likely be given 2 boarding passes and the express path card, in SYD.
Your first flight will be dom so you have to go to SYD T3 to check in, showing passport, even though your international flight does not depart till MEL. But as its a linked ticket, you need to show it to staff in SYD.
Fly to MEL.
In MEL airport, depending on VA Pier A or B, once you get there, find your way to a Travelex booth, go upstairs there, there are stairs and escalators. Your bags should be through routed, without you having to recollect them. Don't go down to dom arr, go up to int dep ASAP as you get to the Travelex booth.
EDIT: thought OP was going to Abu Dhabi, don't know where that came from!!!
If you have your boarding pass and express path card, just go to immi.
Int dep should be the sign.
Its all undercover, on the inside, so you don't have to go to the roadway.
Air cond and carpeted, should be few mins.
Go through the man checking boarding passes and passport. He stands there by himself.
Then go through xrays.
Then go through Aust immi control.
Hopefully they don't pick to body scan you, but body scan is done by the guards, and not Immi or Customs.
Then you are into the duty free section, don't make eye contact with the sales girls or guys, if you don't want to buy.
As one through routed ticket, its a sinch, not as bad as coming back, then less than 2.50 hours might be playing it fine.
Your SYD to MEL flight is VA, yes? And not QF, or JQ.
I have done ADL to MEL to AKL, in 2 hours transit time in MEL.
I am telling you, once you have it er, once, you would wonder why you were so worried.
Do come back and tell me if I was right, or wrong!
EDIT: is the MEL flight to LAS with DL?