It most likely depends on the conditions, awards and agreements of individual workplaces. It most likely also depends on the rules about paid and unpaid leave. It is always a good idea to find out all the conditions, awards, agreements and rules about workplaces and also any possible government assistance or benefits.

I would say that you most likely wouldn’t be able to get employment elsewhere as you are still under contract with the company who you are on maternity leave from. That being said, provided your employer remains unaware of you getting employment elsewhere, you may be able to. But if you are getting entitlements from Centrelink, then that’s a whole other kettle of fish.
If you are needing some more money, you might be able to get cash in hand work and then no one is the wiser so to speak.

I believe you can work so many hours while you are on mat leave however i am unsure if you can work for a new company or whether it is only your current employer. It is best that you research the Centrelink website or give them a call for the right advice as every state could be different and it would be beneficial for you to receive the right advice for the location in which you live in.