I'm going to venture to guess it'll be far higher than 2x the cost of fuel. A respectable commercial hauler will have insurance, a well maintained rig & trailer, professional CDL driver, a trailer sanitized between loads, etc. The last time I asked around I was given a ballpark of $2/loaded mile, but that was awhile back -- before fuel went up so high.
It'll also make a difference if you want him hauled alone or if he can share the ride with others. Sharing a ride can be cheaper, but then you've got the disease exposure issue. Who knows where the other horses came from. They may have health certs, but IMHO those things are pretty worthless. They only tell you the horse *appeared* to look healthy the moment the vet looked at him. There's no way to know if he was at New Holland auction covered in strangles-sneezes a few days before.
I would suggest going to www.uship.com and obtaining a quote - you will get quotes from several different companies and you can get a good idea of what it will cost, and if you find a price acceptable, you can 'accept' the offer! Best of luck!