There is no guarantee that you can stay and work in Australia. The purpose of a Student Visa is to undertake study in Australia and then return home.
This does not negate your right to apply for a visa to stay and work, something which some of our graduates have been successfully able to do.
If you complete the Diploma of Aviation (Commercial Pilot Licence) and Diploma of Aviation (Instrument Rating) you will be entitled to apply for a 485 Temporary Graduate Visa. Details about this visa can be found here
You may also like to consider talking to a registered migration agent who may be able to assist you with professional advice.
Australia has a strong General Aviation industry and there are jobs however this means airlines recruit from General Aviation (Charter, Flying Schools, Air Ambulance, Corporate Pilots, etc) NOT directly from flying schools. An Australian airline will generally not consider an application from anyone with less than about 1000-1500 hours flight time with 500 multi engine hours. It can take years of hard work to reach this level of experience in Australia whilst in many other countries you will be considered for an airline appointment with just a Commercial Licence and Multi Engine Instrument Rating. Thus it is sometimes the case that your prospects to fast track your career at home to an airline will be better than in Australia.