Well done Sir!!!
You'll need to go on the right visa to work over there (you used to have to get that outside Oz too). Just go - you could more than fill your time wandering around Australia but suspect you may wish to spend sometime with the Doris. Never been to Melbourne but hear it's a great place. Tell your girlfriend you both need 6 months off to explore at the end of it if possible.
Like you I loved Perth.
Well done to your girlfirend too.