Fly into cairns work along gold coast to sydney then to melbourne from there
Budget: Australia is expensive. Not as expensive as Norway, but about as expensive as Japan. I wouldn't recommend hitch-hiking (it's not impossible but not very common either). Enjoy the beaches, but either do you research unless you want to only find the crowded tourist-trap beaches or go during the weekdays when they're much less busy (unless it's a particularly hot day, then it will always be busy).
Me and my girlfriend currently living in Melbourne, St Kilda. Always looking to meet new people if you come here (from UK)