Paws & Claws, the kennel here, is very good. Our two cats stayed there when we first arrived. The staff is very attentive, and the facilities are clean. If your pets have to stay there, it won't be a terrible experience for them, and you'll still be able to visit/walk them every day.
And don't panic, when you go through customs in Narita the official there will look at all your paperwork and determine from that what the quarantine time is. If all the paperwork is in order and the timing for everything (shots, FAVN) was correct, you (and your poodle) will be fine.

Also, wait time depends on family size of course, and what rank your family is. We were told it was a 6-9 month wait when we were in the states. We got into housing within 2 weeks. With our own choice of either a townhouse or tower. Now, I understand that's not the case as the townhouses are currently being renov'ed. HOWEVER, there is not a large amount of us from Sasebo up here. Maybe if you try with the Group Sasebo Navy Wives and Girlfriends, you might have an easier time.