Under what visa are you expecting to work? This is an important question and the most critical point in discussion. (I'm assuming you don't have permanent residency as otherwise bringing up your citizenship wouldn't be relevant, right?). I believe pilot is on the skills shortage list so you should be able to sponsor yourself if you want (general skilled migration), but there is a lot of time and expense in that. Is your question whether a bush flying company etc. would sponsor you for a temporary long-stay visa? I can't answer that but I think you need to be clear about your situation.
(I'm a foreigner working in Australia under a subclass 457 temporary visa, but not as a pilot.)