If memory serves me from my last trip there from this summer Virgin Australia flies from Brisbane, Qantas flies from Cairns both into Port Moresby, but since whichever carrier you would need to use to get from POM to Hoskins (Air Niugini or APNG) can be so unreliable, you might be safer having the whole ticket on Air Niugini as a safeguard towards helping with problems if they arise with any of the legs so you'll be all on one airline. Same day connections all the way in or out can often be dicey. You might also get a break on the baggage allowance on the domestic leg if you have the international ticket on the same carrier.
It sounds like you already have your international air into Aus purchased, but if you somehow do not, might be worth looking at purchasing your ticket on Qantas or Virgin all the way through from the States to PNG to save money. If there is a choice on a domestic leg between APNG and Air Niugini, APNG is the more reliable of the two.
The good news despite the hassles is that Papua New Guinea is amazing both below and above the water and you'll have a great trip!