Yes, have done it in the past. These days you need to have the right bits of paper and insurance unless you are working direct through an Accountant. I think you need a Cert 4 in finance at least to be able to practice and it is a good idea to go to the Austwide Taxation/Payroll Course (they issue the fabulous blue book every year, which is so useful for anyone doing accounts). Check out the ATO site for bookkeepers:
Bookkeepers - home

It is a tough gig getting the clients. A lot of small business either don't want to pay what you are worth, even though you can do it in less than half the time it would take them, or they have a "thing" about others knowing their business. I found an accountant who was happy to refer to bookkeepers and he got me my main ones. Once you get going (the hard part), then it is easier to find clients. Get to know some other bookkeepers, sometimes they pass on clients if they are too busy to take them on.