Call the health department where you are moving (city or county, I don't know how Washington does it). Ask them what the licensing requirements are for dogs.

#2 piece of advice:
Print out Flylady's moving tips.

#3 piece of advice:
If you are using a U-Haul, go to the U-Haul website and order the packing kit for the size house you have (it's accurate, I've used it). If you are using a moving company, look them up at www.bbb.org first.