The rear springs "look" not quite up to the task, although I think you'll be surprised how stiff they really are.
Not saying you won't want/need to add something, but wait until the camper is loaded and then full, ready to camp and see how much it really sags and also will give you some time to analyze the rear suspension options as there are about a half dozen different ways to go with it.
Add a leafs, bolt on.
Roadmaster
Timbrens
Sumo Springs
Air bags
Upper stable loads
Lower stable loads
All are a bit different in characteristics or adjustability.
That said, a sway bar will be, not mandatory, but highly desirable. You could add that now, knowing that you'll want that regardless of what you do to take the sag out later.