Is it legal to land aircraft in national parks and state forests in Australia?
The answer to your question, is yes and no.

CAR 92 (1) states that:


  An aircraft shall not land at, or take-off from, any place unless: ... (d) the place... is suitable for use as an aerodrome for the purposes of the landing and taking-off of an aircraft; and, having regard to all the circumstances of the proposed landing or take-off (including the prevailing weather conditions), the aircraft can land at, or take-off from, the place in safety. 


As you can see, you are able to takeoff and land away from a proper aerodrome provided it is safe to do so. As you can see here, misjuding this level of safety can be fatal. 

The Civil Aviation Advisory Publication (CAAP) 92-1(1) provides guidelines on what constitutes a safe landing/takeoff field other than an aerodrome. These safe areas are known as Aeroplane Landing Areas. Although the CAAP is only a guide, it is highly recommended that any area you choose to operate from meets these minimum standards. 

So you are allowed to takeoff and land outside of an actual aerodrome. But your question includes national parks. The rules surrounding these are outside of my knowledge (and they vary from state to state) , but I do know that many parks carry restrictions on vehicle entry, and the types of activities permitted. I would therefore find it very surprising if you received permission to land a plane in their park (if you found a safe landing site in the first instance).   

EDIT: Some commercial flying is permitted within national parks. For instance, they use helicopters and a person on a sling rope to collect crocodile eggs in Kakadu. Obviously then some activities can be approved in a national park. I'd say it all depends on the specific park and the activity being performed. Private flying away from an aerodrome? You would have to check. In any case, my answer to your question is you can land out bush somewhere but possibly not in a national park.