Applicants who have an occupation identified on the Western Australian skilled migration occupation list (shown below) may be eligible to apply for Western Australian State Sponsorship using the following visas:
Skilled – Nominated (subclass 190) visa or Skilled – Nominated (Provisional) (subclass 489) visa
Don't get too excited, you won't get WA Government sponsorship unless you have a potential employer
resident in WA. Your B737 time will not get you work in WA.
I suspect to have any hope of WA Government sponsorship you would need to: a) hold a CASA ATPL and CIR; b) have significant command experience on Fokker 100, Dash 8 or other aircraft types owned and operated by West Australian operators; and c) no Australian applicants for the positions.
And there are conditions attached to those Visas. It will be a long time before you can move anywhere, except of course, overseas again.
It is not impossible to live and work in Australia, but the process is far from simple and you will need particular qualifications and skills which are not currently available from Australian applicants.
Read Centaurus post. I don't think 4,200 FO B737 hours and no GA experience will cut the mustard.....