To be honest, your preference is the last thing you should consider when it comes to new grad positions. I don't know the exact situation in your state, but anybody who is short of Australian permanent residentship or citizenship is absolutely the last to consider for new grad in NSW. That is the fact and you can't do anything about it. What you can do, however, like Butterfly_Light said, is to do your best to finish your study and make sure that you can graduate with flying colors and to make sure that you will be meeting the requirements to register after you graduate. Don't wait until the last minute to take your IELTS or OET. You can take them long before you graduate since the results are valid for two years. In the meantime, you can also try to apply for AIN for PCA positions in hospitals or aged care facilities. The relevent clinical experience will definitely help you when applying for new grad position. More importantly, it allows you to establish relationships with people who might help you when you graduate. The same principle applies to when you are on clincal placement as well. Try to know people and maintain contacts. Knowing the right people can definitely make you stand out among the other applicants when you apply for a job.
