I won't sugar coat it - we do have some of the deadliest animals in the world, from snakes and spiders to jellyfish and octopus. Like with any country you visit, you do have to pay attention to your surroundings. Perhaps it's a good idea to view those critters in an aquarium or wildlife sanctuary, and try to avoid them in their natural habitat....
There are plenty of great places all over the country to view the different kinds of wildlife. For example, no trip to Sydney would be complete without a visit to Taronga Zoo or The Aquarium. The zoo is situated right on the harbour, across from the Opera House, offering spectacular views from many places within. The aquarium, located in Darling Harbour, lets you explore an underwater paradise filled with exotic sea creatures.
If you're headed further up the coast to Brisbane, I definitely recommend stopping in at the Lone Pine Koala Sanctuary. It's the world's first and largest koala sanctuary, although they do also have a wide variety of other Aussie wildlife in a natural setting. Approximately an hour and a half north of Brisbane, on the Sunshine Coast, you'll find Australia Zoo - home of the late Steve Irwin "The Crocodile Hunter".
For a truly unique experience, try feeding the wild dolphins at Monkey Mia (a 10 1/2 hour drive north of Perth in Western Australia, or 2 hours by air).
Regardless of where you travel within Australia, there will be plenty of opportunities to see some of our odd creatures.