Hej!
In Australia its work a bit different to Sweden, best way to get job is to write your resume and walk around the shops and restaurants and handle it to the mangers=).
Sydney is a great place to be in, if u like beach life try to live in manly or bondi but u will see a lot of swedes which could be bit boring for some people u travel on the other side of the world and u still see so many people from Sweden.
Grey hound buses is a good way to travel u can get cheap deals, u don't need to panic booking already from Sweden u can come here and go to backpackers travel agency's and get it booked.
In the east coast of aussie, NSW just start to get a bit cooler. many people go and spend sep- dec in QLD north of east coast and work there self down to NSW ( Sydney).
Good luck