I recently shipped my car from PHX to Derry, NH and it was 950.00, they just asked from where to where, made no difference the type of car. It was on an open car carrier. If you ship it with a mover inside a van, it will cost a lot more.
For that distance from Chicago I paid about $400, but my car was driven by an approved driver, not on a hauler. For a 1200 mile move on an auto hauler we paid $600.
We used Dependable Auto Shippers from L.A. to Detroit. It cost $700 per vehicle (we shipped 2). It also went on an open carrier (like the new cars come in) & once it arrived in the Detroit area, it was then driven right to our front door.
I'm sure they have an 800 number you can call to inquire. I believe they are based out of CA & TX but can/will ship from/to anywhere.
We were very happy with the service. Good luck to you.