There's a new system and basically four steps to take, starting several months before your planned move.
• The first step is to have your pet fitted with a microchip for identification.
• Then if it's more than 90 days old, have it vaccinated against rabies with an inactivated vaccine, then given a booster shot more than 30 but less than 365 days later.
• Then there is a blood test at a Japanese approved lab that shows a serum antibody level of at least 0.5 IU/ml. At least 180 days but less than 2 years should have elapsed since the blood test upon your arrival in Japan; plus your pet should be given periodic booster shots, and not appear ill when it arrives.
• You are supposed to notify the Japanese Animal Quarantine Service at least 40 days prior to your arrival. People coming from a designated rabies-free area have a bit looser regulations, as well as animals of US military personnel.
If you satisfy all the requirements the quarantine time for your pet will be less than 12 hours. If your pet must be quarantined, the costs are typically 2500-3000 yen per day for a private company to hold and feed your pet, which will be done at your port of entry, not your final destination. Unless you live a stone's throw away and can feed your friend yourself, the costs can grow quite high. NOTE: Failure to follow proper procedures could be financially disastrous since your pet will have to be quarantined up to 180 days.
Your airline may also have other regulations or surcharges such as cage type and weight, especially with regards to taking the pet with you in the cabin (PETC) or stowing it in the aircraft belly (AVIH), so be sure to contact them a few weeks before your flight. It may cost several hundred dollars to take your pet. For additional data or other animals, please go to the Japanese Diplomatic Mission in your respective country or visit the Japanese government's quarantine page. Be aware though that in Japan most apartment owners do NOT allow cats and dogs.