Pado,
We traveled a bunch with our Dachshund. I pull a trailer and had her "port-a-pet" tied on top of the trailer. She sort of enjoyed the first trailer we had, but it had a spring suspension. She'd go and was ready to go at a moments notice, but you could tell she was going because she didn't want to be left, not because she REALLY liked it. I first started with her "house" tied onto the rear seat of the jap bike I rode years ago. She did fine with that.
She then started having back problems (unrelated to the riding), so we upgraded to an air ride suspension trailer. She LOVED it!!!!!! When ever she even thought the trailer was coming out, she was standing at the back waiting to go. When it was hot, we'd wrap freezer packs in towels (which later were upgraded to a "wife-made" ice pack bag, that held several in specific positions) and when it was cold, we had a large denim bag that we'd put her house in. We'd let her stay out when it was hot until the last moment to help cool her. She didn't like being the last loaded AT ALL!
I did keep my exhaust stock on the ultras to protect her hearing, but even when I was pulling her trailer with the wide glide (rather loud exhaust- it's my bar hopper), she never seemed to hold back when put in her house. Since we've now got 3 pooches, we must board them or go in the bus.
Go for it, your pooch will love it! Start with short rides that end up someplace fun, ice cream or the park. Then move to longer rides as they get used to it. Gabbie ended up going for as long as any day trip we wanted to take, up to about 750 miles one way. We never went further, trying to minimize her back stresses, but I think she would have gone to Alaska with us if she could have.