This came about because of some failed rebellions in the Canadian colonies in 1837.

After the rebellions were put down, John Lambton (Lord Durham) was appointed by the British government as Governor-General of these colonies. Among other tasks, he was asked to investigate the causes of the rebellion, and propose methods to prevent colonies rebelling again in the future. To borrow from Oscar Wilde: to lose one set of colonies may be regarded as a misfortune; to lose two sets looks like carelessness. The British government had already lost one set of colonies in 1776; it wasn’t looking to repeat the experience.

Durham prepared a report which was published in 1839. I found an online copy of it here. In short, he proposed creating a single parliament in Canada to govern the various colonies (which would become provinces under the proposed new federal government).

The Canadians didn’t get their government at that time; Lord Durham was not in favour with the British government, and he had resigned as Governor-General by the time he published his report. The colony in New Zealand beat them to it, with their Constitution Act being passed in 1852, making that colony effectively independent. Canada got its federal government in 1867.

So, by the time the colonies in Australia started seriously agitating for their independence in the 1880s, the British government had already given independence to other colonies. Australia had merely to ask. There are benefits to being a younger child – the older kids do all the work of wearing the parents down for you.