Watch the GVW and axle weight on your camper. Most campers don't have much load capacity and tires are often the weakest link. If you tires on the camper are over 4 years old and you are running anywhere near weight limits put new tires on the camper before you make the trip. If you have never blown a tire on a trailer you can't begin to realize how much damage that can do to the camper. Be sure tire pressure is correct and check tires often while you are on the road. Try to travel early morning and evening as much as possible during the summer since roads are cooler. Heat builds quickly in tires and they don't like heat!
I always change tires on my cargo trailers ever 4 years regardless of what anyone says about them lasting 7 years. And even with new tires I have actually had two blowouts in the summer heat. The crazy thing was both times the trailers were almost completely empty?
I know the temptation is their to overload but you are better safe than sorry. If you are going to overload anything overload the U-Haul because they are built like tanks & also if you have a flat it is U-Hauls issue not your issue.