Island Air is still at the HNL commuter terminal and no longer offers any "express" type gate claim carry-on baggage service. Your carry-on bag will need to be within size limits and under 16 lbs or they'll ask you to check bag at the ticket counter (checked baggage fees apply).
I suggest for more info on Island Air's carry-on baggage policy refer to their website at:
http://www.islandair.com/flight-info/baggage
Hope this helps you pre-plan your travels and enjoy your flight to JHM.