Sometimes I take the dog to the park in the dog trailer. I went around a corner just a little too fast, and Millie (my dog) was leaned over (her tether in the trailer was too long), and BOOM down we go! She was completely unscathed, no harm done, but it was a big surprise and easily could've been painful.
So it's best not to go too fast. The trailer might get away from you - around a bend, down a hill, etc.
Here's a youtube video of the incident.