(Image: Cryptid Wiki)
The creature in question is called the Burrunjor, and is said to be a surviving dinosaur. Now, before you think that there is no possible way the Burrunjor could be real, remember that there are sightings and stories of other dinosaur-like creatures from around the world - for example, the mokele-mbembe, kongamato, and others in Africa, "Mounatin Boomers" in the U.S., the Partridge Creek Monster, and more.
Over the years there have been many sightings and stories of the Burrunjor in Australia, including this one from Rex and Heather Gilroy from the 1970s:
"In 1978, a Northern Territory bushman and explorer, Bryan Clark, related a story of his own that had taken place some years before. While mustering cattle in the Urupunji area, he became lost in the remote wilderness of that part of Arnhem Land. It took him three days to find his way out of that region and back to the homestead from which he had originally set out.
"He didn't know it at the time, but his footprints had been picked up and followed by two Aboriginal trackers and a mounted policeman. On the first night of their search they camped on the outskirts of the Burrunjor scrub, even though the two trackers protested strongly in doing so. The policeman hobbled his horse, cooked their meal and then climbed into his swag and went to sleep.
"Later that night the two Aborigines, shouting unintelligibly and grasping for their packs and saddles, suddenly woke him up. The policeman realized at this mount the ground appeared to be shaking. Hurriedly getting to his feet, he, too, gathered up his belongings. Shortly afterwards the three galloped away.
The policeman told Bryan Clark later at the Urapunji homestead that he also heard a sound, somewhat like a loud puffing or grunting noise, certainly loud enough to be coming form a large animal. When asked if he intended to include this in his report, the policeman replied that he would not because he bread that no one would believe him.
"The policeman warned Bryan Clark never to return to that area, because if he got lost there again he would be 'on his own': the police would not come looking for him."
The Burrunjor has been known to attack and eat cattle, and several reports describe this happening.
In 1957, a group of 50 cattle were upset by something near the McArthur River in the Northern Territory. The ranchers there didn't know what was happening, and were even more perplexed when one of them ran into the river screaming. They heard a loud grunting/snorting noise, and saw the silhouette of a "tall monster" disappearing into some nearby scrub. The next day the ranchers found several half-eaten cattle.
The same thing happened in 1980, when something was killing cattle, and apparently carrying them off, too. A rancher, Charles Waterman, saw a "fearsome, mottled, 20-foot tall beast" carrying a cow as he hid behind a bush. Other ranchers decided to go after the creature, and did so. They went searching with dogs, and when they got to a river the dogs started acting strangely. After the dogs ran off, the men found "reptilian trackways." They also decided to leave the area.
Aborigines also have stories and drawings of the Burrunjor, like the one below, that look decidedly like something like a T-Rex.
Is the Burrunjor really a living dinosaur? From the reports, it definitely sounds like one. I would not think it to be impossible for a relatively large theropod dinosaur to remain hidden in Australia.