Apart from Crocodiles and Cassowaries in Queensland, and the occasional kangaroo, there's nothing really as big as a bear, or a bobcat, that can kill you here. Not unless you count Great White Sharks.
So, the average human is definitely the apex predator in terms of nothing out here is really actively trying to hunt you unless you're dumb enough to go swimming in some out of the way river or swamp; you wanna go touch a baby Cassowary, because the parental unit is like an overprotective velociraptor throwback; or get between a buck kangaroo during rutting season, you should be safe.
Creepy crawlies, on the other hand, are an ever present danger if you go out looking for trouble, though. There's lovely funnel-web spiders up New South Wales way, and the motherfucker's bite can kill you if left untreated. Then there's the teeny tiny red-back spider, which has a telltale red streak on its back as a warning for a reason (also, notably one of the only spiders that builds three-dimensional webs to catch its prey).
Do you remember the film Arachnophobia? Those deadly spiders? They're common spiderbros over here, go by the name of Huntsman. They're a solitary hunter, typically come out at night, and when they feel threatened, they arch their forelegs in the air as a defensive posture as seen in the film. Their bites are non-lethal, unlike the film in question.
Snakes, on the other hand, are too dangerous to risk hanging around trying to identify. Most of them are venomous. Some of them will outright chase you away, so you better have a good carido regime. That said, in my 30 years of living in and out of urban, suburban, and rural, environments, I have yet to ever see a snake firsthand. I'd be absolutely thrilled to see a reptile thriving in any of these environments given the impact colonisation has had on Australian native flora and fauna.
A good rule of thumb with bugs, snakes, anything dangerous, is to leave it alone, and for the most part, it will leave you alone. Don't poke it with a stick, try not to antagonise it, and if you have to venture into their environments for whatever reason that might be, don't be surprised if you actually find one of these magnificent creatures just going about its business.
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In comparison to America, however, I'm much more frightened of your wildlife. I've seen The Revenant, for starters (/s). Then there's the possibility that any mammal at any given moment could be carrying Rabies could bite you indiscriminately (there is no rabies virus in Australia, so far). There's ticks, some of which carry Lyme disease over where you're at (there's debatable research floating about about whether or not we have our own variety of this disease in our ticks, hooray!). Those rattle snakes you have look pretty cool, spiders, too. Alligators, which are like miniature crocodiles, how cute. And then there's always the average joe blow redneck proudboy incel that may or may not be packing, which I never give a second thought to in Australia (but, sure, we got our our bikies, our bogans, our yobbos, but they're our yobbos, and we understand them even though we don't necessarily approve of their yobbish tendencies).
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Many of the major cities are established around points of water for a reason. They started out as colonies, just like your colonies. The British sent away ships to America, and the British also sent ships away to Australia, but for different purposes (penal colonies, and one actual colony in Adelaide, as far as I remember from history class). Sydney, Melbourne, Adelaide, Brisbane, Darwin, Perth, Hobart, all located around bays/estuaries. Water is a precious resource here, think Dune (not appreciated in the same way as Dune, but it should be). So it made sense to set up shop around water sources that were easy to access. Further inland, it's flat, dry, arid - not outright inhospitable to life, just life as we comfortably like to know it. We have some mountains, sure, but they're glorified hills in comparison to yours.
The southern states, Victoria, Tasmania, enjoy cooler temperatures (but with climate change, the summers get longer and drier every year, and rainfall gets less and less). New South Wales is warmer, more temperate, getting hotter. Queensland is downright tropical, has full blown wet and dry seasons, same with Northern Territory. South Australia is a bit of a mixed bag, I personally never know what to make of it as a state. Then there's the big half of Australia, Western Australia, which is very hot in most places, and again, cooler on the coast, and easily accessible by colonialists from the coast. Every part of Australia has its own flavour.
As far as population distribution goes, a quick Google search says around 7 million people live in "rural Australia", which is anywhere outside the major cities. So that leaves approximately 18 million people everywhere else (out of a total population of 25.36 million). There are hundreds of country towns that range in the hundreds to the thousands to the tens of thousands of people (or more), as centres generally for agricultural hubs, and mining hubs.
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TL;DR Behind every stereotype there's probably a story about some poor bugger who had to take a leak in a public toilet and spotted a big ass Huntsman minding its own business. And, yeah, they're pretty damn big.