I've never taken my dog to Hawaii, but I have heard about the issues. I'm not sure that it's still true, but Alaska Airlines was once the only carrier to allow pets in cabin. Here is info about them.
Traveling with Pets | Alaska Airlines
Also, if you're flying to Maui or some other items, your pet may be eligible for the direct release program instead of quarantine. Here is a link you may find helpful. I think you could call them to get more information about what exactly you're in for.
Direct Release - Quarantine
I think you might want to consider flying via Alaska airlines for the leg to the islands. I've flown to Hawaii from Texas a few times and from Los Angeles. It's a looonnngggg flight from Texas, about 10 hours. I also think you could consider a petsitter to watch your puppy while you're away, or kennel at the vet. I always use a petsitter in my home and the dogs stay in their routines and they don't get stressed out.
Good luck.