There are quite strict requirements for bringing animals into Japan. I would advise you to take a look at the Animal Quarantine Service for Japan's website for more detailed information, especially this changes on a regular basis. If you want to take your pets abroad, it is also best to start the process well before you are planning the move - because collecting all the relavent paper work is a time consuming process.
It might also make sense for you to enlist the services of a relocation company, they'd be able to assist you in all aspects of your move and take a lot of the stress away from you.
When it comes to Working in Japan a lot of expats choose to teach English. Have a read of this article on Teaching English in Japan. It has a lot of information that will be useful for you.
Best of luck with the move.