It is likely that your employer has a policy on working a second job. Look first at HR policies. Your employment agreement and/or award where applicable may also deal with this issue.

A general issue is whether or not the second job may conflict in some way with the interests of your primary employer. The other issue is whether working a second job will impact on your ability to perform the duties of your primary job. Eg coming to work exhausted because of your secondary job.

There is no specific Law prohibiting a person undertaking secondary employment. There are WHS laws to consider and whether your health my be affected by working a second job.

Further, as you work for a government agency it is highly likely they will have a code of conduct or practice which will have guidelines about seeking approval for secondary employment, and avoiding actual or perceived conflicts of interest in the secondary employment. It is imperative you follow the requirements in this code as that is how your employer will ensure they uphold any WHS obligations they owe to you.Your employment contract or industry award may also contain provisions about secondary employment

Finally, what one does on their RDO's or annual leave is up to them, the employment relationship can not dictate what a persin does in their spare time unless it breaches the code of conduct