How was the Australian government arranged in the late 1800s?
The Commonwealth of Australia was formed when the six colonies federated and Queen Victoria assented to the British Government’s laws setting up Australia. That law came into effect on 1 January 1901. If you are asking about government in those six colonies in the lates 1800’s then you are really asking six questions. Try online searching for national archives of Australia and then go to their developing democracy pages, there are wonderful primary documents there for each of those colonies.