Yeah, the main advantage of two-wheel trailers is that (assuming you get the nose weight[1] and balance right) they decouple most of the load from affecting the handling of the bike. Most of the time[2] you just feel this phantom extra mass under acceleration/braking/climbing. I've had a bit of wobble with my Carry Freedom when carrying very awkward loads (long pieces of wood attached diagonally overhanging the hitch), but nothing that wasn't manageable. A camping load ought to be fine.
Stands to reason that the rear wheel will have a much easier time of it than it would if the same load were attached to the bike.
[1] Insufficient nose weight can cause the rear wheel of the bike to lift under braking, which can be exiting.
[2] Except when the trailer runs over or snags on something (foliage, potholes, debris, Silly Sustrans Gates™, etc), which can result in sudden surprises. Single-wheel trailers have an obvious advantage in avoiding this sort of thing - at least when the towing vehicle is a bicycle.