rabies, Hawaii has loosened up its requirements and you can bring a pet into the state with thorough vet records and after completing an extensive checklist. If you don't have sufficient records, your pet will be quarantined for up to 120 days. The UK, Australia, New Zealand, and Hawaii have never had a case of rabies, so I think that's why they've been so strict.

The Infectious Path of the Rabies Virus

1. An animal is bitten by a rabid animal.

2. Rabies virus from the infected saliva enters the wound.

3. Rabies virus travels through the nerves to the spinal cord and brain. This process can last approximately 3 to 12 weeks. The animal has no signs of illness during this time.

4. When it reaches the brain, the virus multiplies rapidly and passes to the salivary glands. The animal begins to show signs of the disease.

5. The infected animal usually dies within 7 days of becoming sick.

https://www.cdc.gov/rabies/transmission/body.html

That 120 days you mentioned tracks pretty well with the above -- 3 months for incubation, another month to be sure -- but the 10 months it took for them to get their dog to New Zealand is just nuts.