Make your carry on as big as you can without going over the carry on limits. The airline website should have the length/width requirements and weight but generally a duffle bag or backpack is fine. And then take your purse, too. That doesn't count as a carry on as long as it goes under the seat in front of you.
You shouldn't have any problems with missed or delayed flights since it's a nonstop flight but airlines are notorious for losing luggage. Southwest lost my brother's once and it had a bunch of irreplaceable vintage clothing in it.
Have you ever flown?
EDIT: Don't take a computer unless you KNOW you're going to just sit around and be on a computer all day. Which I don't recommend. Hawaii is for exploring! I recommend the Doris Duke museum (it's in her house), then there's a few other great museums about Hawaiian history. Oahu is where the royal family lived, before the United States you know, deposed them. To this day I find the whole idea of arresting the Queen Liliukalani for treason ridiculous. All the Americans wanted was the sugar cane. But anyway, sorry, no politics. Uhm. Also, the Waikiki Aquarium is on Oahu. Let me get the names of the other two museums from my folks.
Note: my brother knows the guy who runs the Doris Duke museum. o.O