It comes down to where you want to put your time and resources - camping, or engineering and managing a solar power system. You can absolutely put together a solar system that could allow your popup to run autonomously. I had a portable panel for my popup that kept the lights on but I didn't have a heater, so your loads are a bit heavier.
Step one would be to characterize the load. For the heater specifically you measure how much power it draws when it's running, then either log or estimate how many minutes per hour it runs overnight. That, plus whatever other loads you have will dictate how big a battery you need. It could be assumed that the battery that came with the camper is big enough to run it for 24 hours but depending on what you run for how often you need to know how much excess or deficit you have.
To replace those amp hours used is the mission. What make solar a less than ideal charging source is there's only a few hours a day panels are putting out anything useful, and it only takes one cloud to stop the show. If your panels are mounted to the camper roof they're not at an optimum angle to get the most energy, plus unless you like your camper to roast in the sun all day, they'll be shaded and won't put out much at all. If you use portable panels you have to lay them out, run wires and move them around from time to time to keep them facing the sun. Then either watch them or lock them together so they don't walk away.
A battery monitor that counts amp hours will really help to know if you're filling up or coming up short. It can also help you economize by knowing what you're drawing and cutting back on a few things if necessary so you don't have to wonder if you'll make it through the night.
All it takes is one cloud to render your solar capacity useless. If you're OK with the idea solar is more supplemental power than primary, things are a bit easier. If you want to be 100% solar you need a lot of panels to maximize your charge opportunities and a large battery bank to carry you through the clouds and night time. My approach to solar is I get what I get during the day, then using a generator around dinner time to make up the difference. If you have enough panels and the day remains sunny you may not need any generator. With my popup I used the power from the 7-pin trailer plug to charge the battery, just let the tow vehicle idle for a while around dinner time if it needed it. But again I only had lights and a radio so solar was usually enough. Living in NM with 300 sunny days a year helps.
My advice would be to start with what you're comfortable spending on it, then setting it up at your house with the battery and a few loads to get comfortable with the day to day operation of the system. You can always add more panel and batteries later if you want but the lessons you learn with a small system are the same.
Mark B.
Albuquerque, NM