Based on recent experience where our dog travelled unaccompanied on KLM from NYC > AMS > NRT, we were only required to complete paperwork for entry to Japan ie final destination and nothing was required for the transit point in Amsterdam.

For clarity, I don't know for certain how your dog would be processed if it is in transit in Japan.

The following site may be of help re importing/exporting to Japan or answering those questions. http://www.maff.go.jp/aqs/english/

You will want to avoid any clearance issues for Japan as entry requirements are time consuming and complex. As full disclosure, we used a specialist agency as part of a recent move as any error in the paperwork is expensive and difficult to amend.
In brief, for entry to Japan, your dog requires:
- two rabies vaccines, more than 6 months prior to entry to Japan
- confirmation that vaccine is effective from specialist lab in the USA, approved by Japanese MAFF
- permission from MAFF to import vet 90 days prior to travel
- a cert from your US vet confirming that the dog is fit for travel; this is then validated by USDA, in the week prior to travel

Regarding travel time, please bear in mind that your dog may be crated continuously for more than 24 hours, from check-in to final delivery after customs clearance. You can attach additional water & food trays to the outside of the crate but that may not be sufficient. This is the reason that our dog travelled via AMS, where it spent a few hours airside at the KLM pet hotel.

Disclaimer: This is my understanding of the Japanese regulations. You should contact a professional for advice on your move.