Got a buddywho hauled his dachschund mix in a Burley. The dog could sit or stand as he pleased. Later, he started using a Yak (one-wheel trailer), and the could could only stand. It seemed the dog developed back trouble as a result.
I have seen a couple who hauls a large (60 - 80 pound) dog in a two wheel trailer behind their tandem. The trailer looks kinda like a little Roman chariot.