Big mammals became extinct on the continent of Australia. According to Guns, Germs, and Steel, how did this impact the history of the people on that continent?

To cobble together an answer to this question, we have to look in a couple different places in Guns, Germs, and Steel.  When we do, we will find that the extinction of large marsupials in Australia meant that the Australian people would have a harder time developing agriculture and would, therefore, have less of a chance to develop a wealthy and powerful civilization.
The first part of the answer can be found on p. 308 in the book.  There, Diamond tells us that there were many large animals in Australia during the Ice Ages.  However, these large animals either died off or were exterminated by hunters when humans arrived in Australia.  What this meant, Diamond says, was that Australia had no large animals that could be domesticated.  The largest animal that could be was the dingo, which is a species of dog.
This brings us to the other part of our answer.  That is, we need to talk about why it was important that there were no large domesticable animals in Australia.  For this, we can look at p. 88.  Beginning on that page, Diamond tells us why large domesticated animals can do so much to help people develop agriculture.  He says that, first of all, domesticated animals give people a source of protein in their diet. People can eat the animals and can get dairy products from some large animals as well.  Next, domesticated animals produce manure, which can be used to fertilize fields, thus making agriculture more productive.  Finally, large animals can also pull plows.  This, too, makes it much easier for farmers to grow more food on a given amount of land.  Without large domesticable mammals, Australians would have had a much harder time developing agriculture.
Throughout his book, Diamond tells us that agriculture is the key to developing a strong and wealthy society.  People who could not develop agriculture were not likely to develop as rapidly or as effectively.  Thus, the extinction of the large animals in Australia meant that humans in Australia would not be able to develop a rich and powerful society.