Liabella,
Here is info on public transport to Melbourne Airport.
Airport travel - Public Transport Victoria
This would only get you to the Terminal though. I mapped out a walk with mapmyrun and it works out to over 7.5km from Tower Rd to the Terminal were the bus would drop you off, so walking from there is not a good option. Maybe a cheap bicycle you can lock up somewhere near there is an idea.
I would contact Melbourne Airport or Melbourne Centre and see if they know of any other service that might run between the two locations.
Personally, if I was in a course I would be happy to pick anyone up on my way from the bus stop, so maybe there is someone in the course who is willing to help you out, most people going onto the Tullamarine freeway would be passing by there anyway.
Have you been given an option on waiting for a course to start in Brisbane or are you locked into the Melbourne course?