Pilots are listed on the Skilled Occupation List Schedule 2, but that seems to be for "applicants who are nominated by a State or Territory government agency under a State Migration Plan.". So can I just apply to an Autralian Airline? What is a state migration plan?
In order to get an unresticted right, assuming you arent married to an aussie or have parents who are permanent residents, you will need to find a state that has Airline Pilot on their state migration plan (only one state is currently offering this). You will then need to convert your ICAO CPL/ATPL to the Australian equivalent, then get CASA to issue you a skills assessment based on your previous work history, then apply to the relevant state migration authority for state sponsorship and finally apply to DIAC for your 176/475 visa. If it is granted you can now seek work in Australia as you (and your immediate family) are the holder of a permanent visa. You'll need to work fast because I believe in July this visa process changes to an "expression of interest" scheme which will make the visa grant process much more drawn-out. Probably also worth checking that you will have enough points to qualify for your chosen visa before embarking on this path using the tools at the
Department of Immigration & Citizenship website.
Alternatively, if you can find an employer prepared to offer you a position under a 457 visa (employer sponsored) you maybe able to obtain residency in the long term but this is not a guaranteed pathway to permanent residency.