I arranged a private shipper with a loose box stall for mine on the trailer. (Do be careful, shipping scams ABOUND on places like Facebook. Do serious homework, check DOT numbers, etc.) Bowie has a chute and can run loose stock onto a trailer, but if your new guy isn’t handleable I’d also recommend a chute of some sort (could be round pen panels from TSC or similar) to facilitate unloading at your destination.
Edit: Also be aware that some shippers will justifiably consider an O’Dwyer horse a “dirty load” and decline to haul them. I may or may not have gotten lucky with my shipper.