Honestly, its just a couple days of camping, so no big deal and nothing special on camping gear except bring 100% DEET, WAG bags, and rain gear (it rains almost weekly in the summer on the Rubicon).
What you Absolutely need are tools and spare parts!!!! On every trip I have made to the Rubicon, at least one rig (usually more) has a mechanical issue.
1) I have never been on a Rubicon run where someone in the group did not have at least 1 tire issue. The Rubicon eats tires, so on top of a spare, you want a GOOD patch kit and an air source to fix popped beads. Also in this category, is the need for a few spare valve stems, lug nuts, and wheel studs. If you have manual locking hubs, always bring a spare hub.
2) Next is axle shafts. The trail is usually littered with broke-down vehicles looking for axles, or bumming a ride out to get parts. If you have a D35, I would definitely bring spare shafts. And you do have the proper size socket for your axle nut, right?
3) Drivelines fail just as much as axle shafts. About half the time a spare u-joint will fix the problem, the other times require a welder for a temporary fix. Bring spare drive shafts if you have them.
4) Electrical issues. Because your jeep is going to run hot most of the time and there are several water crossings, I have seen a lot of electrical issues on the Con. Sensors seem to go like crazy on 4.0l Jeeps, especially the crank positioning sensor which is under the Jeep and will get wet. Also, too many people start the trail with a shitty battery that barely works. Running our winches, offroad lights, and years of hard starts on extreme inclines and in cold weather really tax a Jeep battery. So if your battery is old, it may be a good time to replace before running the con. In modern vehicles, one little 5 cent fuse can cause the whole vehicle to die. So bring spare fuses. And you have a good set of jumper cables, right?
5) Spare fluids. A sharp rock through the oil pan, a blown power steering line from hours of stress in the rocks, a tree branch popping a trans line or getting tangled in a brake line, a crack in the radiator, and having to dump your dif fluid after cleaning up a busted axle shaft. Spare fluids are a life saver. Spare gas can come in handy. Also in this category are items such as radiator stop-leak, RTV blue, epoxy patch, and JB Weld.
6) Steering components. Don't go with a factory Jeep tie rod; there is a 50% chance that it will not last. If your steering stabilizer is positioned below the axle housing (like on a JK), relocate it or it will get smashed in the first hour on the trail. Bring spare power steering lines, these go A LOT due to the stress of days of turning in the big rocks. A spare PS gear box will eventually save the day for you. Always have spare bolts to fasten the box to the frame, these bolts shear often, especially in XJs. Spare tie-rod ends will get used eventually.
7) Belts / Pulleys. A spare belt a must. Also, idler and tensioner pulleys go out a lot. This is usually compounded by crossing deep water and the bearings seizing. These items are cheap insurance, light, small and easy to store.

Suspension components. Suspensions get the workout of a lifetime on the Rubicon. I always bring a spare flex-joint and bolts for my links. Spare leaf spring mount bolts are a MUST if you have leafs as these break often from the stress. The Con eats a lot of rear shocks, especially from backing up in the rocks (which you will do often), so a spare shock and spare mounting bolts are a good idea.
9) Brakes. I have personally lost two break lines on the Rubicon in one trip (with my YJ). Luckily, I always carry 2 spare brake lines.
10) Cooling system. Spare radiator hoses are a great idea. They all go bad after a while, usually in the worst possible places. You also need spare clamps for the hoses.
11) A good "Jerry rig" kit. Baling wire, duct tape, electrical tape, electrical connectors, epoxy patch, zip ties of various sizes, hose clamps, an assortment of spare nuts/bolts, and ratchet straps can fix an amazing amount of damage. This may get used more than your spare parts.
The worst thing you can do is run this trail with a vehicle that is not mechanically sound. Do a full lube and inspection before leaving home. In particular, clean the whole vehicle down and inspect all of the welds on your suspension mounts for cracks. Clean the motor/trans mounts and inspect those for cracks. If your Jeep is overheating or running like shit, DO NOT GO, this is akin to fucking up the trip on purpose - you will be the "blue Falcon" of the club.