I work in Sydney. There is no answer to your question. It depends on the company and the project you are working on. Same as it is everywhere else I expect. Good luck with the new job and welcome to Australia.
Lots of different roles for BAs. Business BA, technical BA (same as systems analyst). QA and testing are often done by specialist test analysts but quite often BAs will do some. Also seeing ads for process analysts. In larger companies often people with the title BA don't have BA skills and are subject matter experts. Basically as a BA you'll get asked to do all kinds of different things.
Agile skills are becoming more in demand. Sydney is big in financial services, so if you have skills there you'll be laughing.
Can't tell you my job description as I'm looking for a new contract at the moment. I work as a business BA mostly.
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