[Legbreaker]

PNG is almost like an extra state of Australia, and was under our direct control until 1975. There's still very close ties, and militarily it's the location of one of the key events in our history - the battles of the Kokoda track.
As mentioned previously, we also send quite a lot of money there to subsidise the government, and a number of Australia resource companies have large scale operations (mines, etc) there.
Note also Australia was the main country to go to East Timor's aid in 1999, well before the UN became involved with New Zealand contributing the second largest contingent, the largest they'd sent anywhere since the Korean War.

Australia's sent troops into the area, and will very likely do it again if needed.

As an aside, back when I was still a reservist and before I went full time, there was a rumour floating about that if Australia sent another 100 soldiers over seas, a reserve unit would need to be activated to maintain the minimum number of troops necessary within our own borders. Can't say how true it was, but given just a few short years later reservists were indeed being called up, given additional training and sent to reinforce regular (full time) units in various locations through the Pacific and I believe Afghanistan and Iraq.
Worth noting too that reservists have NEVER been required to leave our own borders, except for the couple of battalions sent to PNG in WWII and supposedly employed as labourers (of course two of those poorly trained and equipped battalions soon found themselves advancing across the mountains before conducting a desperate fighting withdrawal against 10,000 of Japan's best).