According to Guns, Germs, and Steel how did big mammals becoming extinct on the continent of Australia impact the history of its people?

One of the central theses of Jared Diamond's Guns, Germs, and Steel is the importance of animal husbandry, meaning the ability of a civilization to domesticate large animals like cows and horses for their own needs. He often makes the comparison between Eurasian civilization and Mesoamerican civilization by pointing out the relative strengths of Spanish conquistadors relative to the Aztec Empire in the 1500s. While Spaniards domesticated about a dozen types of animals, the Aztecs had only domesticated the dog. This meant that Spaniards could rely on larger animals for food, as well as horses for transportation, while the Aztecs could not —leaving them a step behind.
In the case of Australia's civilizations, Diamond points out that Australia did have many large mammals during the Ice Age: big marsupials, giant kangaroos, and giant wombats. Yet these "candidates for animal husbandry" disappeared as the animals were driven to extinction, either by human activity or by a changing ecology. The result was an entire island with no domesticable native mammals. Australia, like the Aztec Empire, had only the dog, which was not native to Australia, arriving perhaps 3,000 years ago.

Diamond sums up the effects of the large-scale extinctions of Australian megafauna in this way:

Those extinctions eliminated all the large wild animals that might otherwise have been candidates for domestication, and let native Australians and New Guineans with not a single native domestic animal (44). 

Diamond assigns considerable importance to the presence of domesticable animals, which he sees as indispensable to the development of agriculture. Settled agriculture is the single factor that contributes to the ability to produce the "guns, germs, and steel" that gave some peoples the power to conquer, colonize, and even destroy other peoples. Because aboriginal Australians had no domesticable animals, they did not develop these things, and their surroundings were unable to sustain the kind of population growth that gives rise to civilization. Something similar happened in the Americas, which also lacked domesticable animals, a fact that placed native Americans at a disadvantage when they made contact with Europeans for the first time. This is crucial to Diamond's thesis that environmental factors--essentially accidents of geography--led to pivotal differences in the development of human societies.