Hi,
I don't know if you have already moved but in case you didn't, here's some information.
You will need to go to the department of agriculture for 2 forms. 1 form is your import permit. The other form must be filled out by your vet It's the west nile virus isolation form.
Your bird needs to be quarantined at a vet facility for I think 10 days prior to departure. It must be in a mosquito free area.
Your bird needs to be in a carrier that has wire mesh covering all openings. The mesh needs to be small enough to keep mosquitos from getting to your bird.
It must be transported directly to the airport from the clinic.
I have shipped my blue and gold macaw from california to Oahu. Even though you are going to the big island, your bird still needs to come to Oahu first. I don't know too much of the process because my breeder was doing the shipping. If you go to the dept. of ag website it will tell you what you'll need, and you can always ask them what you're unsure about. It's been 6 yrs since I shipped my bird, so things may have changed.
I would try to get a direct flight to Oahu if possible. The first attempt to bring my bird didn't go so well. My bird had missed it's connecting flight and was sent back to the vet clinic.
Be aware of the time of year that you will be shipping. The temperatures may cause problems.