Growing up my parents were big "campers". We lived in S. FL and traveled to CA with Dog in tow. My father owned his own business and took a month off for this trip pulling a 27' trailer. The dog at the time was a medium sized dog. No problems.
A little later in life he upgraded to a motor home with a Border Collie and pit bull. No problems at all.
I would agree with the crate as I'm a big proponent of them. When your stopped and set up, you could throw it outside. While traveling and/or away from the camper, the dog has a familiar space and your RV is protected from the dog, not anyone that might want to break in....
I think you will be fine. Maybe some short trips to start just to test the waters. You never know.