Convict transportation to Australia ceased in 1867 with the ceasation of transportation to the colony of Western Australia. Already by then Australia was being seen as a destination for free settlers, and Melbourne was in 1837 (or 1835, when John Batman arrived in Port Philip) founded by settlers rather than convicts and their guards and administrators. Although to this day Australians find occasional derogatory references are made to our nation's convict past when we ping pong around the world, by the second half of the 19th century Australia was seen as a land where talent and enterprise could secure a good living - this theme runs through much British literature of the time, and we see it in Dickens' works for example. He uses it as a device to give characters a way out - it was a place where your slate could be wiped clean and a new start was possible.
After a series of conferences, conventions and referendums throughout the 1890s, the First Commonwealth Parliament of Australia was opened in 1901. Much of Australia still looked to Britain as the "Mother Country", however, and appeal to the Privy Council wasn't abolished until 1986. In 1914, Australia would not hesitate to follow Britain into war with Germany and its allies. There was also, however, a strong Irish-Australian contingent, as well as immigrants like my Swedish great-grandfather, other Europeans, and groups such as the Chinese who had come out for the Goldrushes, many of whom remained.
Debates over free trade vs protectionism dominated much of Australia's political scene for the first decade of the Commonwealth's existence. There was also a strong nationalist sentiment, expressed by publications like
The Bulletin, that fostered the "Australia for the Australians" idea - i.e. the exclusion of immigrants of non-Anglo-Celtic background. Legislation to limit immigration had been passed in 1902, and would in time evolve into the "White Australia" policy. It was still a melting pot, though - from Russian Jews seeking to escape pogroms to Irish immigrants like those in my family who sought to escape poverty at home.
Labour had organised following the 1891 strikes into the Australian Labor Party, and this was emerging as a dominant political force in addition to the old Free Trade/Protectionist parties. The Labor Party itself was factionally split along the predominantly Irish-Catholic right faction and the more strongly socialist left faction. The first Labor government was formed in 1904, and in 1912 Andrew Fisher and the Australian Labor Party were in Federal government. Interesting to note also that by 1912 women in most Australian states had the right to vote (Australian Aboriginals were not so fortunate).
Sydney, Melbourne and Perth were all well established by 1912 - the first two had well established Universities, for example, and Perth University was established in 1912. Flush with goldrush money in the 19th Century, they had impressive public buildings, established public art collections, and transport systems and infrastructure. James
Moody, writing in the early 1900s, described visiting sites such as St Mary's Cathedral in Sydney, and he would also have seen impressive government and trade buildings around Circular Quay. Our national capital, Canberra, had yet to move beyond the planning stages, however - the site (between rival cities Sydney and Melbourne) was not selected until 1908, and the foundation stone on Capital Hill was not laid until 1913.
Australia was producing significant scientists and explorers - not only did Aussies join both the Scott and Shackleton expeditions, in 1911 an Australian, Mawson, had launched his own Polar expedition (born in England, his family emigrated to Oz when he was 2 yrs old). Poets, artists - even what was arguably the first, or one of the first, feature length films had been produced in Australia.
Following the visit of the American Great White Fleet in 1908(an anniversary we're preparing to commemorate down here), plans for an Australian Navy were progressed to the point that the Royal Australian Navy was established in June 1911, and the first Australian warship was launched later that year.
So it was a young nation, predominantly Anglo-Celtic in origin but fuelled by international immigration, forward looking in some socio-political aspects but very much suffering from the prejudices of the age in other regards, confidently looking to an independent future but also suffering from insecurities perhaps inevitable in a comparatively small, geographically isolated population...still buoyed by the comparatively recent Federation but regarding itself as very much part of the British Commonwealth of Nations...and about to forge a national identity through WWI (or so the conventional narrative runs!).
Phew - there's a lot more to it all than that, of course. These were early years for the national of Australia, and a time of struggling to find identity and a place within the Commonwealth and the world.