I am on maternity leave and not due to return for another few months, am I allowed to pick up casual work at a different hospital while I’m on leave?

From the Leave Matters for the NSW Health Service policy:

Employees are required to follow requirements in applying for and taking leave. The various types of leave outlined in this Policy

Directive are for specific situations and must be taken for the purpose sought. For example, parental leave is to provide employees time to care for and bond with their children. Sick leave is granted to allow employees to recover from illness or injury, while personal carers leave is available to care for

immediate members of their family who are injured or ill. Employees who plan to take up any secondary employment during a period of leave must seek prior approval.

This means that even when you are on a period of leave such as maternity leave, you would still need to seek approval to undertake casual work elsewhere. Not doing so could be seen as a breach of the code of conduct.