Thousands of rvers travel with their dogs. We have for 5 years - full-time.
Biggest word of advice I have is to spend some time in the new RV with the dog, some of her things, water dish etc and let her get used to her surroundings so that she is comfortable when it comes time for you to take off somewhere.
Most RV parks are pet friendly but some have restrictions for certain breeds, size or number of dogs allowed.
With heat/AC and a radio if Bebe won't bark continuously while you are gone you should be fine. If she makes a fuss or lays in the windshield on a hot day, I wouldn't. Some places do have local laws against leaving pets in a vehicle. Not sure if they would classify a motorhome as a "vehicle" or not.
Take shot records and rabies certificate with you. You probably won't need them, but if you require a vet for any reason they for sure want to see the rabies certificate - same for grooming salons.
We travel with a supply of ear cleaner, shampoo, brush, heartworm and flea/tic meds ( purchase from vet) and a good supply of prescription eye meds she needs, antibiotic cream and benadryl ointment in case of itchy skin irritation or bites.
She may turn out to be a real fan of travel and camping , many dogs can't wait to go when they know the rv is being loaded up.