Things that will kill you:
Blue-Ringed Octopuses + Blanket Octopuses (look them up) + most other octopuses.
Any kind of Snake. Pythons aren't poisonous but they mostly live up north away from Melbourne.
All kinds of Sharks, on all coasts but especially off South Australia and Western Australia.
Box Jellyfish can have almost invisible tentacles up to several meters long, - if attacked, pour vinegar on the wounds, this helps to neutralize the toxin, you might still die though.
Bluebottles (like a man-o-war) will hurt tons if you get stung.
Up north, Freshwater and Saltwater Crocodiles will kill you.
All spiders are dangerous, generally red-back (under your toilet seat, in your boots, around your outside garbage bin), white-tail (bite keeps hurting for years afterwards) or any spider that looks like a small black tarantula (Funnel-webs and Mouse Spiders) are very dangerous. Big horrible things that stay in a large web usually aren't dangerous unless you actually provoke them.
Larger and more aggressive kangaroos (like KeepitClean mentioned) will maul you to death and drown you dog. Do not attempt to ride them under any circumstances.
Magpies (a black/white bird which makes a distinctive gargling call) which are pregnant or nesting (in springtime usually) will swoop down and try to peck your head/face if you approach their nest (which could be in any tree).
We have scorpions in the desert.
Also centipedes, millipedes. Up north they can get like a meter long.
It's unlikely that you will ever see any large lizards, but don't mess with them. Goanas (large monitor lizards) will claw you, Bogeyes (small things whose tail looks like a second head) will death grip your limb until they are dead or your limb comes off. Blue-tongue lizards aren't too bad.
Possums are usually pretty scared of people but don't piss one off obviously.
Koalas are savage and will try to claw you, but only if you mess with them.
Freshwater dams/ponds/rivers (murky water) has large crustaceans with pincers called yabbies. Maybe half the size of a lobster max. They will give you a fun little nip.
Also wild pigs will gore you.
Emu's prefer to run away because they can run really fast, and they mostly live on dry/flat plains out west, but they are as big as an ostrich (that's bigger than you) and will do serious damage to you if annoyed.
Also, if you find yourself caught in a current that carries you away from the beach and out to sea - DON'T FIGHT THE CURRENT and SWIM PARALLEL TO THE BEACH and then back to the beach later. I can't stress this enough, something like 90% of all deaths on our beaches are by people who don't know how to escape a rip current, tire themselves out and then drown.