It depends if the training course instructors are required to be accredited or not. It also depends on the duration of the course. Since it's only a week you should be okay, but you need to verify directly with the flight instructors, to make sure they do not sponsor student visas.
For instance, according to the visa requirements section for "Advanced Flight Theory of the Sunshine Coast Airport", you should not need a student visa for one week of flight training, if the instructor is not accredited by law.
Because we are teaching to a syllabus written by the Civil Aviation
Safety Authority (CASA), there is no requirement for our courses to be
While our ATPL Theory course is accredited, we are not required to be
accreditated so Student Visas are not issued for study at Advanced
Students can attend the courses provided they abide by the conditions
of a visitor/tourism visa.
Check with the training course instructors to see if they are required by law to be accredited.
It is possible your flight instructors are accredited and could be required by authorities to sponsor student visas for visitors. If this is true, in this situation you may be required to get a student (study) visa. It depends on how they are registered with the Australian immigration authorities for sponsorship.
Since you did not specify the instructors or company providing you and your friend the course, it is hard to say for sure. It's best to verify with the instructor that a tourist eVisa is acceptable, to follow Australian law.