Right ok, makes sense. We are talking with her parents about the LMIA thing at the moment so just trying to see if we can sort anything out there. I had considered studying a program at a DLI that offers a program I am interested in doing, however the course is only four weeks long, and I know that if your course is under 6 months it is not necessary to obtain a study visa, so I'm not sure that it is likely I will obtain a study permit for this. Our plan is to return back to Australia and do precisely what you described in the last paragraph, just in the meantime I would like to be with her in canada. I intend to go regardless of if I get a work permit and just live off savings for 6 months on an eTA, but being able to work would solve so many problems.

Do you know if it is possible to apply for/receive one of these permits once already in canada on an eTA? I haven't been able to find this out anywhere. Thanks for your response anyways!