We've got black widows here, in the U.S., which are related to redbacks. They're not really a big deal. IIRC, there hasn't been a reported death from a black widow bite since 1982.
We don't have anything like the funnel web spiders, inland taipan, eastern brown snake, or salt water crocodiles (unless you count grizzlies, but they're nowhere near as aggressive). Also, the box jellyfish species we have here aren't as dangerous as what you've got down there.
I think I read that there hasn't been a death from the funnel web spider since 1981, so I guess that kind of falls into a category similar to our black widows to some people. They're way, way more aggressive than our widow spiders though. Those fangs are nuts!
Of all the dangerous animals in Australia that I'm aware of, the salties are what I'd be most cautious about.
As an American that has read up on Aussie wildlife and statistics about their lethality (from Australian based sources), I think the media sensationalizes things. Most Americans have a distorted perception of the dangers posed by Australian wildlife.
I think this is the same thing that happens when other parts of the world look at the United States and firearms. The media skews reality.