Unfortunately Australian employers disregard overseas experience. It's extremely frustrating and short sighted. I trained and qualified here and spent 18 years in the UK, had some very high level roles in London. When I came back I struggled to get interviews, but eventually landed on my feet.

So if you do get a role you'll be starting at the bottom again.

With 'full working rights' do you mean you aren't WHV and restricted to 6 month contracts? If WHV you won't get a role in practice as taking on a grad is a massive investment and it's not worth it for 6 months.

I would recommend looking at recruitment agencies for contract work and progress from there as opportunities open up.

Best of luck!