I live in one of the places you are visiting. Happy to PM if you want to talk more specifically.
I don't specifically *worry* about any of the things you mentioned but I (and most Australians I think) do take sensible precautions. None of the creatures you mentioned are going to hunt you down and attack you but all will defend their personal space and territory if invaded.
Box jellyfish - only an issue during stinger season (October to May) in northern waters. So Sydney won't be an issue. In Cairns they should only swim in within stinger enclosures if they plan to swim in the sea. Hamilton Is is probably the same but it may be far enough off the coast that stingers are less of a problem. The local staff will be able to advise.
Snakes - only an issue of they're tramping through the bush. If they plan to bushwalk they should wear long trousers and solid shoes and watch where they're going but it's not a big deal.
Spiders - as long as they don't stick their hands into dark spaces or dead logs etc they're unlikely to encounter any poisonous spiders.
Crocodiles - not an issue in Sydney. Around Cairns they should avoid swimming in estuaries at dawn and dusk or in rivers big enough to have crocodiles in them. Everywhere is well signposted if it is a potential crocodile habitat.
In reality, if they want to see any of those things, they're going to have to go to a wildlife park or on a "spotting" tour.
I have lived in Australia all my life, some of the time in very rural areas and I have never seen a deadly snake or spider in the wild and I've only seen crocodiles at a distance. But I do take the precautions I mentioned above.
I've also worked in Emergency depts for the last 10+ years and I think I've seen one spider bite (gardener not wearing gloves) and one snake bite (person whose job it was to relocate poisonous snakes). According to the venon research unit there are only about 3 snake bite deaths a year. The last recorded spider bite death was in 1979 as we now have antivenom for both of the potentially deadly spiders.
So, pretty long-winded way for saying that I don't think you need to worry I'm happy to talk more if you want to know anything else though.