I've flown from Darwin a couple of times (but only with AirNorth, and not very recently) and never seen any queues that would be anything close to one hour. It is a small airport with only a handful of international flights. If I recall correctly (but don't take this for certain), there is not a real separate international area airside, but you'll wait in the domestic departure area until close to boarding time when you go through the passport control to a small waiting lounge next to the gate serving international departures.

In any case, especially with this many connections and little prior flying experience, it would be wise to be at the airport well before the departure time so there'll be time to sort out any remaining or emerging questions.