With you a bit of luck, you can get a job in the industry. However, enjoying it is another matter. One of my friends worked at the airport for a company that manages a private fleet of jets. He was around planes all day, but all the work was all admin-related work: setting up the maintenance schedule etc. He hated it, and went on to become a consultant (which he did for a while before becoming an air traffic controller).
In Sydney, there's very few aerospace jobs. The most obvious one that comes to mind is the air force - a few years back one of my old classmates was working at Richmond RAAF on the F16s (or F18s, can't remember). And while it's true that there are foreign aerospace companies in Australia (e.g. BAE, Boeing, Airbus Group etc), most of the work will be maintenance-related, and any design work is usually very limited in scope (e.g. upgrading a small component of an aircraft).
The Aus Space Agency will not be like other conventional space agencies. There will be no rocket launches, and their focus is on satellites and on management/policy. It just seems like they've just gathered all of Australia's space-related industries under one roof and formed a central body. Apart from that, nothing new. Personally, I'm not too optimistic when it comes to how they'll impact the space industry - seems like more hype than substance, but let's hope I'm wrong.
Now for the big leagues like NASA, Boeing, etc, I've got much to say. For starters, you'd have to move overseas to do that, as I'm sure you've heard. However, there's one small catch that many people don't realise or they conveniently leave out: Aerospace is inherently a defence-funded industry. The only difference between a rocket and a missile is that one has a person sitting on top, the other has a warhead. Hence, you'll notice that all overseas job applications at any of the major aerospace companies will all state the same thing: Only candidates with US (or whatever country) citizenship and eligible for a security clearance (which typically requires you to have at least 10 years of verifiable background history) will be considered. This means that it is extremely, EXTREMELY, difficult getting into places like Lockheed, SpaceX, NASA, ESA without some connections and someone pulling some strings.
The most viable way to get into that industry is probably through NASA as a research scientist, since they employ post-docs (which don't need a security clearance) for research, after which you might be eligible to become a PR. To get a post-doc position at NASA, you'd need a PhD (4-5yrs) from a US institution (or local institution, but you're chances won't be anywhere near as good) typically in a related research field. If you want to move away from research and go into corporate engineering at Boeing, Lockheed, etc then you'd need to obtain citizenship since that definitely requires security clearance. Even being an engineer at NASA requires you to be a citizen (or PR at least). NASA is a government agency, so they only employ US nationals. The only exception is JPL, which is privately managed by CalTech, so they have leeway in hiring foreign nationals (although they still must be residing in the US with a valid working visa at the time of application). However, their international intake is still EXTREMELY low (since they must be approved by the higher ups). Also, the foreign nationals are placed and restricted to work in some warehouse on the campus, and they were extremely limited in where they could go and what they could work on.
All in all, moving overseas to obtain a PhD for the CHANCE of a post-doc at NASA, and then for a CHANCE of getting into the big leagues as an engineer, is a massive commitment to say the least. This is the path I originally took - I was doing a PhD over there on a research project funded by NASA, and I even had job interviews with NASA JPL since my research was closely related to what they were doing. But not long after I started, I decided it simply wasn't worth it. Nonetheless, it was a great experience for me, and I don't regret anything since I gave it a a shot and decided it wasn't for me. And while I'll get to work at NASA next year, I got in through a very unconventional and selective process, and it's definitely not permanent.
I should also mention that if, as an academic, your research is revolutionary and you're a pioneer in what you do, there's reasonable chances that you could work on projects with NASA etc, which would make it a lot easier for you to work for them down the road. However, again, this is down the academic side of things, but tends to be the most realistic road, since getting into private overseas aerospace companies is next to impossible.
I know I've probably burst your bubble, sorry about that - I wish I knew someone who could have told me this earlier on while I was at uni. Keep in mind that these jobs are very romanticised. Like my friend who worked with private jets at the airports, there will be jobs, even at NASA, that are mundane and will make you hate it. Designing the next generation aircraft/spacecraft doesn't happen often, and when it does, only a very small select team will be involved in the design process - the rest of the engineers will be analysing the stresses acting on a bolt holding down the toilet during takeoff. So I'd recommend that you don't base your career aspirations on that infinitesimal opportunity.
I'll just finish this off by saying I got friends who have worked at NASA, ESA, etc, and they left since they weren't happy with it. So, my advice is that you should just find a job which you enjoy. Investing 10 years to get into that prestigious job at wherever is no guarantee that you'd enjoy your work (or even like it) any more than a job back home. I'm also not trying to discourage you from doing aerospace. If you love aerospace, by all means go and do it. Just know that there's plenty of jobs out there which you can land, and be happy with, even if it's not what you originally aspired to do.
Hope this helps.