Welcome from a dog lover. We have a rescue, long hair Jack Russell, Maltese mix, Snoopy.
Waste water dumping...good disposable gloves, black water first, then gray water, then rinse well. Fresh water...rinse the tank first with fresh water and some white vinegar, empty, then rinse with just water. Let dry out a bit, then fill it while checking the levels. Obviously you will need to get to a dump station for the dumping, but you can probably do the fresh water at your home. If this is your first experience, camping in your own yard or driveway first can get you in the practice. Set up, run everything, break down. Make notes.