If you are not crossing international borders to enter Hawaii, then you would have to follow certain rules for taking your dog to Hawaii. First of all there is no restriction by airlines on taking small dogs , cats or even domestic birds as carry in luggage. But you would definitely have to meet quarantine requirements. The quarantine period is 120 days, 30 days or upto 5 days, depending on the kind of Rabies test. For detailed information about quarantine rules here is a link:
Hawaii
Hawaii
