I would like to bring my Chihuahua to Hawaii. She is microchipped, vaccinated for rabies, and licensed in California.
Can I bring her to Hawaii?
Does any airline allow in-cabin pets on flights to Hawaii?
From Hawaii Pet Passport & Import Regulations (not an official site so take it with a grain of salt), yes you can take your dog to Hawaii. However there seems to be quite stringent requirements both before and after arrival.
Hawaii has a five-day or less program for bringing cats, dogs and ferrets into the state. The program is designed to allow pets that meet certain qualifications to be released immediately upon their arrival at the Honolulu airport. You must start the process not less than 120 days prior to arrival in Hawaii in order to qualify to avoid quarantine.
So with care you can collect your dog as soon as you arrive. Without care you may find your dog impounded in quarantine for the duration of your trip. Also note that it looks like you must fly into Honolulu unless special arrangements are made in advance - which may affect your travel plans.
You may enter Hawaii through Honolulu International Airport only between the hours of 8 am and 9 pm. Your pet will be taken from the airport to the quarantine center. You will pick up your pet at that location. Pet owners should be sure to arrange for their flights to arrive in Hawaii by 3:30 p.m. The process of clearing your pet generally takes one hour if your pet conforms to all requirements and has arrived on a direct flight. Otherwise, the process can take up to 4-5 hours. Pets not cleared by 4:30 p.m. will be held overnight at the Airport Animal Quarantine Holding Facility.
You may also enter through the neighbor Island airports of Kahului, Kona, or Lihue but special arrangements must be made in advance. Note that not all airlines participate in this program. All requirements for entering Hawaii must be met and documentation must be submitted at least 30 days prior to import.
As for the airline question, the answer is yes in general, but that is going to depend on the airline in question.
I live in Hawaii and I brought animals from the mainland and they have to have gone through the 120 day quarantine process before they can come in.
You cannot just bring them on the plane with you like traveling within the US. It is super strict with no exceptions. If you just wanted to bring your dog on vacation with you it is not worth the hassle, just board them at home.