there is no such thing as a visa exempt application! You get 60 days visa free if you are from one of the 90+ countries that can do that. You can even extent your permission to stay for an additional 30 days. You just need your passport a plane ticket and a toothbrush and you are good to go.
can I ask why? What can you use the pink ID card for at immi that the passport can't? Nothing I presume - except you don't have to bring your passport and the pink ID card is obviously always on you.