The Indonesian island situated just northwest of the Australian mainland is Bali. However, this statement requires clarification: Bali is actually part of the Lesser Sunda Islands and lies roughly 1,100 km (680 mi) north of Australia's Kimberley coast—not immediately adjacent.
If "northwest Indonesia" refers to the country's northwestern extremity, that would be Sumatra (specifically Aceh province) and the Andaman & Nicobar Islands (Indian territory) near the Strait of Malacca.
For travelers: direct flights connect Perth/Darwin to Bali (Denpasar) in 3–4 hours.