Edit: I realise now this was necroposting, sorry.
It's difficult to tell from what you've stated your situation. You may well have a degree, but what have you done since that degree, and how did you end up migrating to Melbourne? Are you an Aussie or not, and if not what is your visa/right to work status?
Like it or not your age would be relevant. If you've spent a year "finding yourself" since the degree, not too much of a big deal, but if you've been on an extended walkabout for a number of years that's going to be rather harder.