You must meet all of the following requirements to be eligible for streamlined student visa processing:

At the time of making your student visa application, you must have a Confirmation of Enrolment (CoE) with a university or non-university higher education provider participating in the streamlined visa processing arrangements for a:
◦Bachelor degree
◦Masters degree
◦Doctoral degree
◦Non-award university student exchange program
◦Non-award study abroad program.
•If you enrol in a package of courses, all your preliminary courses must be at an education provider participating in the streamlined visa processing arrangements or a nominated educational business partner of that provider.
Note: If you combine a non-award university student exchange or study abroad program course with any preliminary course(s) you will not be eligible for streamlined visa processing and will be assessed according to the applicable assessment level.
If you are sponsored by the Australian Department of Foreign Affairs and Trade or the Australian Department of Defence on an AusAID or Defence Sector visa (subclass 576), you are not eligible for streamlined visa processing.

Refer: http://www.immi.gov.au/Study/Pages/Streamlined-student-visa-processing.aspx

A list of universities and non-university higher education providers participating in the streamlined visa processing arrangements can be checked on DIBP website.