Back in 2001 I looked into shipping a car from Georgia to Oregon and believe it was 1500 dollars. Could be 2000 now not sure. You should google it and find some shippers and E-mail them for an estimate. I assume you are talking about Wash state and not the District of Columbia. Here is one I found, but do not take this as an endorsement, just one of the first to pop up on google, but has an instant estimator.

http://www.nationaltransportllc.com/...FRqYiQodtFCGQA