Firstly, how far into your degree are you? Many Aerospace engineering grads go into car design or anything that has an aerodynamic aspect to it. Australia really isn't at the forefront of aeroplane design unfortunately. One of my colleagues is a former aero engineer, he used to sign off B747s and the like. He prefers flying and has just made captain, but also uses his engineering skills as a reg & tech guru writing procedures for special airports etc. Another string to his bow.
What do QANTAS want? CASA ATPL, Command IR, unrestricted passport, Class 1 medical, appropriate experience. You gain the experience through instructing (if you don't want to leave Melbourne) and moving through the ranks that way, ideally Grade 1 flying instructor with multi engine and IFR teaching credits. If that doesn't appeal, then you pack your car and head "up North" to places that hire low time pilots. (That's what you'll be once you've finished training. You should have at bare minimum, a CPL with Night VFR. For the bigger aircraft, you'll need the ATPL subjects and an instrument rating). The bare minimum will qualify you to fly day VFR charter in probably a C206. Then it's the hour build/gain experience -> move to twins -> turbine etc. However, you'll hit the numbers when the QF hiring cycle begins.
Right now, QF and most airlines in Australia won't need new pilots for a while. They might in about 5 years time - just a guess.