When I raised dairy calves, we have hauled a bunch of baby calves in the back of a pickup with a top/shell or whatever you call them. Have also hauled several goats, sheep, even some hogs. In later years I got a Goat Gopher that I could easily take out of the truck bed in order to utilize the truck. That made it much better as I wasn't as limited as with having the top on it. There is a stockyards is n the mountains a couple counties east of here,Bon sale nights the parking lot would be full of small pickups with makeshift crates and racks, mostly to haul goats or hogs.
For on farm hauling a calf to the barn we now use our Polaris. My wife drives it and I hold them in the back.