Being from Melbourne, I'm always interested to know what people think of Australia.
The overwhelming impression I get is that people believe this country is full of interesting and highly dangerous stuff. That's true, to an extent. Even the trees can kill you during summer - they drop entire limbs when sufficiently stressed. The east coast cities aren't too different from their counterparts in other Anglophone countries, except that they're much quieter and there's funnel-web spiders which can bite through shoes in the northern states.
Once you figure out the golden rule (i.e. don't touch or go near anything unless you know it isn't dangerous), it's a nice place to live. Aside from the lamentable politics, of course.
EDIT: Oh yeah... we have lots of anti-venom, too. No-one has died from a funnel-web bite since anti-venoms became available 30 years ago. Just don't get bitten by a snake and you should be okay. Avoid the cone snails, box jellyfish, stonefish, crocodiles, sharks and blue-ringed octopi, and the beach should be safe.