I'm in CA... Usually pay around $1000 ballpark from the Midwest. But if you email some of the good shippers like Sharrway they'll be happy to give you a quote. Less $$$ is not always best though... It's precious and delicate cargo!
If you're on FB, I run a Florida transport group and multiple shippers are on their regularly. Post your need and they'll bid for your transport. https://www.facebook.com/groups/318453711563208/ you just have to join the group to post.
I paid $800 for Skip to travel 1,200 miles from WI to MA, and later paid $600 to get Kandy here (I got lucky and found a private person who happened to be trailering through WI on their way east, and just wanted help with gas $$$). I'm going to echo disneyhorse and say definitely check out the company/person first!
BE CAREFUL who you use! There are some not so well known or that contract under a big name that take your money and dont deliver! Or the shipping conditions are not great.......