Is it true that Australia was originally a British colony?

This is completely true. Although the Dutch were the first to explore the coastline of the Australian continent, they did not colonise it. It was colonised by the British for two main reasons:

1. To expand the British empire, and prevent the French from gaining a foothold in the Australian continent or in that part of the Pacific. The British were at war with the French and seeking to colonise more lands in order to gain more power and influence.

2. To solve the problem of Britain's overcrowded prisons (a consequence of the Industrial Revolution) by establishing a new penal colony in a land which showed promise for eventually becoming self-supporting. Britain had been sending their excess prisoners to North America, but the American War of Independence put a stop to the practice. Following this, the English were no longer able to transport surplus prisoners who couldn't legally be executed to North America.

Australia remained a British colony from the time the First Fleet of convicts landed, in 1788, until Federation in 1901. Even then, it was still subject to British authority until the Australia Acts of 1986 completed Australia's path to independence.