A.P.
Get him checked by your pediatrician to make sure he doesn't have a cold/ear infection before your flight. For me, that would determine my decision about traveling with my own toddler.
The pressure in the eustachian tube is what causes the pain, and it affects them mainly when they have a compromised tube (from allergies, infection, or other irritation) and the tube cannot clear. If your son has an ear infection or sinus issues, I would not take him on the flight at all until fully recovered, but if he does show up with a slight infection or problem, the doc may give you appropriate meds that will help clear it up enough in advance.
Otherwise, the flight shouldn't bother him if he is swallowing regularly or sleeping. He might become bored though, and crying can make the pressure more intense.
If you bottle feed or nurse, this seems to work wonders on the babies I see on my long flights, because it's cuddly and they are swallowing/clearing the eustachian tube regularly.
13 months is also old enough that you could bring toys and books and maybe a DVD player if you don't have an appropriate in flight movie or VOD in the seat.
Also, I would take the car seat so he has a familiar seat that he can nap in and so you don't get tired of holding him on a longer flight.
Have a great time in Hawaii!