Molokai - Maui looks close: perhaps 46NM unless I've missed something. That should take a lot less than 45-60 minutes.
As an indicative look: EMB-120, off a 4500' runway in 30 degC temperature (ISA+15degC), elevation 400', nil wind, dry runway, PW118A engines: should be able to takeoff at 10800kg. That will take 22 pax and 3 crew on that leg, which is a bit less than full capacity.
However, I keep bumping up against questions that can only be answered by an aircraft performance engineer (which I am not). The wet runway performance will be less than dry, which means fewer pax. The landing distance graphs show that on a wet runway, it will severely limit the weight and pax load (and may be worse than takeoff). There has been no consideration yet of climb gradients. And not all EMB120s have the more powerful 118A engines.
All in all - the operation is a possibility but is marginal and only a close look by an aircraft performance engineer can give you the correct answer. Time to pay someone to do some work for you.