People taking their birds long distances to shows use all sorts of carriers, everything from "official" chicken show cages to cardboard boxes to rabbit/small animal cages to dog crates. I would suggest trying to keep each bird separate as they sometimes begin pecking or fighting each other, and you probably will not be able to stop and intervene--if you even know it is going on. For my wire cages, I have built dividers that I attach to the back side with zip ties (so that it is hinged at the back), and once the bird is in place, fasten the front with gem clips or more wire ties. Show cage cups are accessible through the wire for filling, and with wire sides, there is more ventilation. Cardboard boxes or other solid sided container needs ventilation holes. Sweet PDZ or food grade DE will absord spills; Sweet PDZ is better at removing odors as it chemically alters the ammonia. Both are safe should the bird eat it.
If you have waterfowl, they are usually moved in lidded rubbermade tubs half filled with water, with lots of air holes all around the top edge.