If you are to apply for an Australian University you need to do so via their International Office which Swinburne will have on their website where they should be able to answer any questions that you have before making an application.
You need to check with them as to what your status is in terms of whether you can apply or not.
You will need to apply for a Student Visa which allows a person to be in Australia for the duration of their studies but you will need to return home upon completion as there is no automatic granting of permanent residency in this country as that is a separate application.
Most student visas are issued for those studying a university degree, not diplomas or certificates as they do not count.
You should also include the fact that you were not successful for Canada and the reasons why, it pays to be honest with your application when responding. It may mean you will have to pay a refundable bond to the Immigration Department which is held until you leave the country as required.
This was not fraud but clearly you did not provide sufficient or reliable evidence that your intention was to study and not take advantage of the system.
Part of the visa application will require you to provide certified copies of financial support, that is you have to show that you are able to support yourself without any work for a period of 18 consecutive months.
The Australian Government does not provide any financial support to International Students or non-citizens hence the reason why you need to demonstrate that you have the funds not only to cover study expenses but living costs as well such as food, accommodation, travel, clothes, rent, utility bills and so on.
If granted a Student Visa there are stringent conditions attached, any breach of those conditions will result in cancellation of the visa and immediate return (deportation) to the country of origin. A student visa does permit some work to be undertaken no more than 20 hours per week during semester and up to 40 hours per week during the non-semester period.
The work that is available is not the best paid, generally commissioned based, long hours with days all over the place.
All Australian universities have student performance monitoring and reporting in place and have systems to check with students as to what is happening should they start to slip behind so be warned that if you come here and are accepted that you are here to study and not play the system.
Australians are generally pretty friendly and welcoming, but they do not tolerate anything that is a clear abuse of the privilege to be here.
Two links below are from the Australian Government websites:
Study in Australia
Department of Immigration:
Hope this helps.