Australia per se was never a British penal colony. Australia was six British colonies, and while the first of them (New South Wales) was largely founded as a penal settlement, for others (e.g. South Australia, Victoria, Western Australia) penal transportation played a minor or absent role in the colonisation process.
Why did the British establish penal transportation to Australia? The American Revolution had meant they couldn't transport convicts to their North American colonies any more - the US would no longer accept them, and they were too worried the Canadians might rebel as well to send any more there. I'm not sure whether it is true or not that 20% of Australians are descended from convicts (Wikipedia makes that claim but provides no source for it), but whatever the true percentage is, some portion of Americans will be descended from British penal transportation to America as well.
