Started riding with a pooch last year. Started with just a cardboard box bungeed to the back rest and seat. Have a harness for him and connect that to one of the bungees. After about a 1000 miles and the dog loving it, I built a wooden one. Every time a Harley rumbles by the house, the dog starts bouncing off the walls. He LOVES to ride.
Recommend take a couple of slow rides in a parking lot till the animal is used to it. They will try to bail a couple times. Our dog adjusted really quick. I get more smiles from people when they see him than I could ever imagine. Logged around 5000 miles with him last year. Both of us are anxious to better that this year.
Good luck with it!