There are a bunch of companies that do this. One thing to be careful of is that some may say they ship enclosed but they purely broker it out whoever is cheapest and then the final leg may be enclosed. Not sure if they have a route from FL to CA but my first stop would be Intercity Lines. They do a great job and don't farm it out, they transport the cars themselves. Here is the contact info.
Roy Sewell
Sales Manager / Driver Recruiter
Intercity Lines Inc.
www.intercitylines.com
roy@intercitylines.com
800-221-3936 ex202
If they don't travel that route they will know someone else good that does.