I would think that externally accessible storage and an external shower/hand wand would be key. You won't want to be tracking sand and salt into the camper (at least try to avoid it as much as possible).
Externally accessible, but secure rod and tackle storage, a place for folding chairs and a bucket, your rod holders, sun shade, and a dedicated wing table for cleaning fish (unless you would prefer to keep that operation further away, then a small portable folding table and/or large cutting board might be preferred). I know some guys can clean a large fish pretty much right on the spot with little more than a fillet knife, but I'm not that good at it and prefer a clean flat surface to work on.
Shoe storage near or just inside of the the door with a mat that attracts, or a container that collects sand. It would be nice to have the spray wand hose both near the fish cleaning station and also near the entry door for washing sand off feet before entering.
If fires are allowed on the beach you probably will need to haul your own fire wood, or settle for one of those propane pits. Dedicated storage capacity for either of those would be something you want to plan from the beginning.
The 4-link suspension really shouldn't be needed since all trailers rotate about the hitch with only 2 tires and 3 points of contact, having independent and/or articulated suspension isn't the same as on a car or truck with 4 points of contact. Sure, the Timbren style or trailing link style of air bag suspension can afford more ground clearance under the middle of the camper, but is the extra complication really worth it? How much ground clearance do you have under your Jeep's axles? You can achieve the same thing (more actually) by running the same wheel and tire combo on a straight leaf spring or rubber torsion axle. What is important, with the short wheelbase on 2 door jeeps and if you plan to run up and down dunes (steep approaches, crests and drop offs) is to get an articulating hitch; either a simple pintle hook and lunette ring (some say are clunky, but easy to hitch), or one of the universal joint style swivel hitches (quiet but can be more difficult to align when hitching). The typical ball and socket style hitch that I measured only had about 22-23 deg up and down articulation.
Whatever you decide to do, good luck and have fun.