After finishing aero eng., I went overseas. Obtained a design authorisation in my company, amongst other qualifications/licence. Have done a fair amount of work in certification, mostly as PM.
As suggested, I'd be approaching design organisations (CASA website should have a list, although I'd still search under CAR 35). You could also approach design orgs in Europe, the US, or NZ, or try to get into OEMs overseas. (Around a quarter of my cohort ended up in Europe at an OEM, but that wasn't through UQ).
Try to track down the design orgs providing services to airlines in Australia - I know that there are a few very interesting projects going on at the moment, although I don't know that graduates are being hired (work experience might be possible, or just ask if you could visit for a coffee & chat).
Working airline-side can also be very interesting, although, again, you may need to look overseas, and if you get in, you may need to work to get into the right position (and then practice patience - projects don't tend to turn up every day).
Getting a practical familiarity with aircraft maintenance can also be a benefit - if you want to design &/or certify parts and systems for aircraft, it's a very good idea to have some knowledge about the travails of maintenance staff, keeping aircraft airworthy, and ease of installation/access, etc.
It is a fairly niche market, especially in Australia, and you might find that you are doing other (design & certification related work, or ops work) more than just FTE work.