If you're bringing the dog, I'd recommend against flying. Transporting animals via planes (unless you can bring it onboard with you) is pretty cruel IMHO.

Commercial airlines are not deliberately cruel or even particularly careless when it comes to shipping dogs; they just aren't set up to deal with pets efficiently. Unless a dog is small enough to carry on board the plane, air travel is a risky way for it to go.

The basic problem is that to an airline, your pet is just an especially bothersome piece of baggage. And as everyone knows, baggage slip-ups are inevitable, given connecting flights scheduled too close together, long delays, and human error in a stress-filled, overloaded system. When a mistake means your luggage goes to Minneapolis while you go to Atlanta, you'll survive the inconvenience. But if your dog goes to the wrong city or is forgotten on a luggage carousel, it may not survive.

One additional thing that you maybe hadn't considered. Why not rent an RV where you are and drive it to the West Coast? There's a lot of pretty country along the way.

If you are RV-ing it...definitely hit the Olympic Peninsula. La Push (hit the tidepools at low tide: A-freakin'-mazing), Hoh Rain Forest, Crescent Lake, Hurricane Ridge, Port Townsend. Ignore the Twilight fangirls and it's still a great place to recreate.