Hi Caitlin and Sanji, the best time for cruising boats to head out of New Zealand, bound for PNG is April, May, June. There are two regular routes. The first via New Caledonia and the second, across the Tasman to the east coast of Australia, then north along the coast, inside the Barrier Reef.
The coastal route is by far the best scenic choice; the New Caledonian route, the quickest. At this time of year, monsoonal activity across the tropics makes voyaging potentially very dangerous. Tropical revolving storms (cyclones, hurricanes, typhoons) form with great regularity and prudent sailors will not make the trip until the threat of TRCs have ended.
Meanwhile, keep sailing. Experience is desirable but not as important as compatibility. Good guys get rides, with or without experience. However, navigation skills are always welcome, as are good cooks and people who can entertain themselves.
Best of luck in finding a suitable boat heading north.
"if at first you don't succeed....Redefine success"!