The 2 main GHA's in MEL are Menzies & QANTAS. I don't think you'll get much of a run at QF, but I was wrong once before.
Look up MenziesAviation & get the address for the Ops Manager (Peter) & let him know what you're after. He's a straight up chap who'll set you straight & won't BS your hopes.
There are also a number of Bond stores if you're interested, besides QF & Menzies. Australian Air Express, Patricks & DHL have airside depots that might be worth a look. Then of course, you could try any Freight Forwarder & that's your best shot for mind.
I seriously doubt you'll get a gig on the headsets at the pushback tug. This job is predominantely done by LAME's.
Why not look up Avalon airport & see who's got the contract down there? It's a bit further out of MEL, but might be a goer.
Bon chance!
