If you're in the cities, you'll not find anything hazardous. Unless you're in Sydney where they have funnel-web spiders. Which is yet another reason not to visit Sydney
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But I've been in the bush plenty and the closest I've gotten to anything dangerous is passing copperhead and tiger snakes (both among the top 10 most deadly in the world) whilst hiking. But it is true that they're more scared of you then you are of them.