Commercial Pilot is not currently in the
Australian Skilled Occupations List. This means Australia does not have a skills shortage in commercial pilots and that occupation will not assist you to obtain any Australian resident working Visa.
In effect, the Australian Government considers there are enough Australian Commercial Pilots living in Australia to fill current requirements.
An Australian airline
may make application to sponsor overseas pilots in a specific category/with specific qualifications and experience (e.g. for the introduction of a new aircraft type etc) if it could demonstrate an immediate skills shortage in that category of commercial pilot and it had taken steps to train Australian pilots to fill that requirement in the longer term.
There is certainly no guarantee the Dept of Immigration and Border Protection would approve the Sponsorship and Visa application.
The fact that an aircraft normally domicile in Australia has US (or another country) registration would not be justification for employing overseas pilots. Immigration would probably point out to the operator that he has two options to address his pilot needs, register the aircraft in Australia or send Australian pilots overseas to obtain their foreign licenses.
Unless a US citizen commercial pilot holds alternate qualifications, skills and experience in a skilled occupation in demand and is prepared to work in that alternate employment on arrival in Australia, the only option open to you would be to join 565,000 other US citizens that visited Australia last year as tourists for non working stays up to three months.
Working Holiday Visas are also available to US citizens but there are a number of restrictions, including age, and employment duration. You would not get commercial flying work in Australia on a Working Holiday Visa.
Australia's immigration laws are very similar to and generally a reciprocal of the US immigration laws.
The short answer, unless Australia buys the Space Shuttle, a US commercial pilot has very little chance of obtaining an Australian employer sponsorship and a work and residency Visa based upon his occupation.
You could think about marrying an Australian, however to be granted a Spouse Visa you must demonstrate a relatively long term committed relationship. A quick turn through a Las Vegas wedding chapel simply won't cut the mustard.