You don't have to be a citizen of Australia to get a job, just have permanent residency etc. It would seem that you've got that angle covered with another skill.
As you've hinted at, it's not a simple process to go from flight school to jet FO. Or even turboprop FO for that matter. You can get a job as a pilot with 250 hours in Australia. It won't be on any thing fancy, if you're willing to shift to a remotish part of the country it will be on a C206 or something like that.
The conversion is comparatively easy going to Oz. Note, our instrument rating requires the NDB to open it.
There are only a few jet operators in Australia and (unfortunately) a lot of pilots competing for those jobs (often) with thousands of hours on turboprops and the like. Networking is vital over there.
Many of my friends "back home" will not get the opportunity to fly a jet for various reasons. None of them are because they don't have the ability.
Chances are you won't be on any "nice & shiny" aircraft for quite some time in Oz but the flying & scenery is second to none and while it's hard work, it's a lot of fun.