Yeah they would have compasses, sextants and maps with the known continent and islands on it. I was planing that the airships are like football shaped hotair balloons that supports large basket like bottoms with a few propellers, run by steam power at the ends. They can't land on water, but they can tie the airships off at sky docks, which are a ladder into the sky with pillars and a boardwalk. (Think like a regular dock, but it instead of it stretching over the water, it stretches over cliffs, or just built platforms raised up a hundred or so feet.) The sky ships were designed to pretty much only hop from island to island around the known continent. (These islands are for the most part Hawaii sized. ) There are a quite a few islands scattered out around the known continent, places where others live, and airships are like community transit between these places. To travel to the other side, you would need massive amounts of luck to come across, and if someone ever found it, (I'm thinking yeah, maybe a few airships from the known continent stumbled upon it.) the perils of heading back to the known world would be too dangerous, since the discoverers of the unknown continent were most likely in horrible skeleton-like shape when the new world was bumped into. Food was most likely running out or rotting or gone, water would be rationed and the men would be dehydrated, and perhaps even mechanical failures could be happening since it would take months upon months upon months UPON MORE MONTHS to find. Not to mention a water world like this would be incredibly stormy, windy, rainy, and unpleasant. lol. The continents are Australia-sized if not smaller, so exploration here is much like 'looking for a needle in a hay stack.'
The resources? I'd say they are well stocked for materiel resources. Tropical rain forests have all the wood, food, and water one would need. What they don't have much of, is housing in the big cities. Land is running out where one could live, and talk of logging out some of the islands the land bounds get their resources from, so if this happens, then there goes the neighborhood. lol.
Dragons and sky sharks? Fucking awesome, and yes. lol