Sorry to hear just keep plugging away sticking to their application format. Keep a look out for private hospital nurse jobs as well as SA Health. I think you may stand a better chance in Australia and I dont think they are big on feedback but that's no comfort to you at moment. I know what you mean you couldn't afford too long without job and it's difficult to even go without employment but people do. Persnally I probably couldn't manage for more than a month without a job.
Are you stating in your cover letter you are PR and when you coming to Australia? I would also state you are prepared to arrive early if offered job. The CV and cover letter is your only opportunity to tell them your personal curcumstances.
The way I would approach this is keep applying for everything even if you think it's not for you or suitable. If you get to Australia without a job start applying for all nurse jobs straight away. Even go through recruitment agencies if you have to. While you wait on those applications just apply for other jobs, care work shop work, bar work, anything etc just to tide you over until you get what you want. Personally that's what I would do.