An egg-laying animal is called oviparous. There are many oviparous animals in Australia. All birds, as well as some reptiles, fish and almost all amphibians lay eggs, as well as many arthropods.
If the question means which mammals which lay eggs, the answer is monotremes. The only known monotremes are the platypus, the short-beaked echidna and the long-beaked echidna.