Australian Biomes. There are three major biomes in Australia. Each has it's own organisms and climate. Tropical: this consists of a closed-canopy rain forest or eucalyptus forests with mountain ash and gum trees.The cold tropical rainforests in the Melbourne area were spectacular.Marsupials include: koalas, opossums, platypus, flying foxes,and lyre birds.ropical: this consists of a closed-canopy rain forest or eucalyptus forests with mountain ash and gum trees. The cold tropical rainforests in the Melbourne area were spectacular. Marsupials include: koalas, opossums, platypus, flying foxes,and lyre birds.