Neither Denpasar nor West Timor is a country; Denpasar is a city on the island of Bali in Indonesia - and is nowhere near PNG; West Timor is part of Indonesia - and is nowhere near Myanmar.
Of the other two choices, Indonesia has been a nation since 1946 - it became independent from the Netherlands, though Japan was involved in the process; Indonesia was occupied by Japan during World War II, and the nationalist sentiment for an independent nation was largely the result of this, and the declaration of independence came only very shortly after the end of the Japanese occupation. 1946 doesn't make Indonesia "one of the world's youngest countries", though. Over half of the countries in the world have become independent since that time.
East timor *is* one of the world's youngest countries, though. It became independent from Indonesia in 1999 after a long-running civil war, having been part of Indonesia since 1975.
I'm a geography expert - also, my cousin served in the peace-keeping forces in East Timor