Baymule
Herd Master
Bigger is often better. There is animal transport insurance where if you have a flat or trouble, supposedly they get there faster because of the animals. In a trailer, they would heat up fast. Maybe an animal transport would be a better idea. How many miles, how many hours, can you drive it straight through?

This is why I make sure to carry a hose with me when transporting livestock. Also, if you can get hold of some 5 gallon Sparkletts type bottles, carry those with you to water the animals during the drive. If your goats are still in milk, bring a portable stanchion and milking equipment. Stop at a truck stop and park in the back then you can milk on the road. Dump the milk if you have no way to strain and refrigerate it. Be prepared for the goats to yield less milk for several days after the trip due to stress. (Experience from transporting dairy goats to and from shows all over southern CA.)