I certainly support Jenn's comments. The mention of servants etc in the diary may indicate that Emma travelled as an unassisted immigrant ie she paid for her own passage. I have searched the assisted immigrants shipping arrivals and there is no ship arriving Nov 1884 at Port Adelaide with assisted immigrants.
Coastal shipping was very active between the states, not only for passengers but for cargo. Emma mentions
in the train. She would have travelled on the first Government built and owned steam railway in the British Empire which commenced in 1856 between Port Adelaide and Adelaide.
Emma was only one of thousands of young woman [including my gggrandmother] who emigrated to Australia. My gggrandmother was unable to purchase a passage to Melbourne, so opted for Adelaide and then travelled to Melbourne on a coastal trader, where she arrived in 1854. Her story is not in a diary but related by her to my father.
Our ancestors were far more mobile that we imagine.
I always find it helpful to read the social history of the era you are researching. South Australia was not a penal colony and as Jenn as already mentioned, transportation of convicts had long ceased.
Just my two bob's worth
Cheers
Cando