My first job in analytics was in large part luck. I had an academic background in Physics and Mathematics, some professional programming experience building applications and self-studied computer science. I searched for "python" jobs, since I liked the language, and applied for a job titled something like "Awk, Bash and Grep". I didn't get that job, but was forwarded on to the data engineering team building bespoke reports. That was at a medium size company called Hitwise that provided digital competitive insights.
At the time I had never heard of Hitwise and had no idea of the kind of data processing that they were doing. Now I've got a few more years of experience in the field and know quite a few more people I'm aware of quite a few companies that do analytics in Melbourne. But there must be dozens more that I've never heard of doing interesting work.
How can we find companies doing analytics in Melbourne? Silverpond have a (incomplete) list of organisations working on AI in Victoria in their 2019 MLAI Survey on pages 19-21. Searching the organisations many of them have had representatives present at Melbourne Analytics (for example here's a past agenda). A few of these have presented at Data Science Melbourne, for example on how to be a Data Science Consultant, Startup Data Science and other talks.
This gives a reasonable starting point for a walk through analytics companies. Look for appropriate conferences, courses and events in the analytics space. Follow up speakers, sponsors and attendees and the companies they work for. Look at who works at those companies and where else they have worked. To get real depth start talking to those people and finding out more about them.
Another approach for finding medium to large companies is to monitor job postings. Keep saved searches of relevant analytics terms and start collating the companies that appear.
I think it would be really interesting to map this out at a high level; but it's going to take a lot of work.