Sorry to pipe in late here Jake,
Monash University offers Astronomy as a straight major degree option. They have a great Astro department and their own observatory. They are also second to Melbourne Uni regarding statewide rankings for Universities (not that that really matters). Nonetheless, you most certainly can study a Bachelor of Science (Astronomy) in Melbourne at Monash University.
http://www.monash.edu.au/pubs/handbo...-astrophysics/
I looked into everything that was offered some time ago when I was thinking of returning to uni to studying Astronomy. I wish Monash offered off-campus options, then I would be set
Hope that helps.
Ralph