Although the world's dinosaur history starts in Triassic period, the first Australian fossil records are from Jurassic. We know, however, that dinosaurs were in Australia during Triassic, because there are fossilised dinosaur tracks in Australia that date back to Triassic.
Australian Jurassic dinosaurs include Ozraptor and Rhoetosaurus. Both are from mid-Jurassic. Ozraptor is a carnivorous dinosaur that walked on two legs and was much smaller than the massive Rhoetosaurus - a Sauropod found near Roma in Queensland. Sauropods are the largest animals ever found on the Earth, with long necks, small heads and herbivorous diet.
The Cretacean dinosaurs found in Australia are much more numerous. Carnivorous dinosaurs (Theropods) include Timimus, found in southern Australia, and Kakuru, famous for the fact that its bone turned to opal. Minmi, found near Roma in Queensland was an armoured dinosaur (more exactly a nodosaurid); and Kronosaurus, found near Richmond in Queensland was a pliosaur (a marine dinosaur). Two Ornithopods (herbivores that belong to the bird-hipped, as opposed to the earliest, lizard-hipped dinosaurs) are Muttaburrasaurus, found in the outback Queensland; and Leaellynasaura, found in Victoria (which during the Cretaceous period was situated in polar region). An example on a cretaceous Sauropod (the massive, long-necked herbivores) is Austrosaurus, found near Winton in central Queensland, where many new findings have been made relatively recently.
NOTE: This website is written in British English, which is the English we use in Australia. You will find words like "traveller", "harbour" and "realise", and they are all correct in the language used in Australia.