Riding with your pet is always going to be fun, but i cant imagine something like strapping my pet to the sit or making him sit into a box or carriage where he might be really uncomfortable, is cruelty to them better way is to ensure that you make your pet really comfortable with the vehicle and give him short rides, so that they are relaxed and start enjoying being there.
I was fortunate in that I got Suzi as a puppy and was able to familiarize her with the bike before she rode it for the first time. At that point, I used liver and chicken treats to get her used to the bike, then running bikes, and of course having friends drop by got her very excited about hearing motorcycles and seeing riders in gear and helmets.
I had her ride in a backpack for the first few trips, then found that having her in front of me was the best as I could watch her interest in the ride. She hated speeds over 70 kph, possibly too much for her nose? I'd another dog that pulled her head in from the car window, so I was expecting that. The most trouble I had was pulling up to a stop waiting for a long light with idling cars, and she didn't appreciate the exhaust fumes and became agitated right then and there, but later on accepted that we would be moving again and it never occurred again.
I did have an issue with a car load of young teen aged girls. They rolled down their window at a stop and got excited about Suzi in her Doggles, and Suzi wanted to bail and join them in the car but was attached to me via carrier and harness.
I purposefully made the trips short and at low speeds so she would learn to love being on the bike. A weeknight ride at 60kph around the neighborhood and to a dog park met with her approval.
Fast forward to the second season... She'd already been out to PEI to my sister's place on the bike the previous year, and this time around the weather was just so hot that we both had trouble beating the heat (ALWAYS carry water on your bike for the dog!), and she started to leave the carrier with her front legs while riding under 60kph in and around town. I called it tank surfing, then she started doing this on the secondary roads between the small towns, as long as her doggles were on and we did 90kph or less, she was totally in her element, sniffing out manure piles, seaweed and dead fish along the coast.
I found that while I can do an 800km day on the bike, it was a bit hard on her, so if we had to go further, I'd have to stop more frequently and she was reluctant to get back on the bike. In Napanee, about 3 hrs from home, I felt like a cretin loading her onto the bike for the second last time, and when we hit Oshawa, I was apologizing to her and telling her we'd be home in an hour.
That being said, when I get ready for a trip, and bring out her carrier and harness, she makes sure to follow me outside and wait anxiously until she sees me approach her with her harness in hand.
Unfortunately the the DR650E has a pyramid style tank, so we may have to redesign a platform atop it where she can rest her forelegs, so until such time she can't ride the bike, and that is highly unsatisfactory for us both.
