Against my better judgement I'm going to comment.
First some background.
The story goes that when I was an infant my Dad took the family camping.
Mom would not sleep in a tent so Dad set up a sleeping bag in the back of the station wagon.
When Dad woke up in the morning he could hear somthing was up, apperently while it was still dark I woke up hungry and started to crying.
The baby bottles and formula where in the ice chest in the tent and Mom was too scarred of bears to get out of the car in the dark.
So Dad woke up to a wife and baby crying and realized right away that we were done camping.
As a child I have great memories of camping in a home made tent trailer set up to tow behind a Jeep Wagoneer and Mom was happy.
So I get that some time the obvious choice is not so simple.
The next obvious choice
If it's avalible, don't drag your house with you, rent it at the destination.
This doesn't work if your hanging out with
@Montecresto on his version of overlanding - there is no hotel half way there.
Some 12 years ago I had a business trip to Utah.
One of the hotels we stayed at was along the Piute trail.
There where several ATVs staying there that night.
They rode the trails during the day up in the mountains and dropped down in to towns along the way at night.
Given the right trail system this seams like a good mode of operation and it could be cheaper than buying an overlanding trailer.
However I realize that this advice is probably wasted on most of the people participating in this thread.
Actual relevant to this topic stuff.
I would recomend to keep any trailer concepts simple.
Yes there are trailer suspensions designed for off road but how good are they?
Looking at the Boonie Stompper i would estimate it's going to have some teething problems.
The trailing arm IRS systems with a good track record are designed for axles weights well above what is indicated for a p500 trailer.
Way over build for what you are looking for.
And, if your not a chassis systems design expert I would not recomend trying to roll your own.
The last thing you want is to find out you made a small error in design while far from your truck (ie. In the middle of nowhere).
My recommendation would be to use a solid trailer axle with a 3k lb rating.
I would guess the loading for suspension off road would be ~ 3X the on road rating.
You can get the axle built to the width you want with a 4 on 4 stud pattern.
Use the leaf spring designed for that axle but remove leaves to match the weight .
(I have a flat bed trailer with a single taperd leaf, totaly high tech but inappropriate for this application)
I know some have dismissed solid axles in the thread but I belive that are simple and functional.
The ground clearance is only 1/2 the tire hight.
But a p500 on stock tires only has 8.5 inches of clearance, how much more do you need.
Also get a square or round pipe axle, not a U-channel or (heaven forbid) angle iron.
(This rules out a harbour freight special)
As for the trailer format, somthing like a small land scape trailer with a low roof top tent rack would work well.
You could use plastic totes to store gear (and be weather / dust proof).
And a few water / fuel cans could be placed over the axle.
This link shows the basic idea but a poor execution.
This guy used a harbour freight trailer as a basis and it failed on the trail.
Also, he was towing it with a power wheels...