I've seen a few trailers that didn't have suspensions claiming that the bikes suspension was sufficient. I also ran across a cheap trailer that surprised their new owners with a 45 mph limit after it was delivered. I would put a suspension on any trailer I built. In fact last year I considered building my own bust didn't because I'm in the middle of too many projects already. I started a thread about six months ago about trailers.
Here's a site that sells tailer parts...
Portable Generators, Heaters + Wood Stoves, Snow Blowers, Pressure Washers | Northern Tool + Equipment
One option might be to buy a trailer kit and use the parts such as lights, hitch, suspension, etc. to complete your own. Northern tools has a few for about $250, a little light duty however.
There are quite a few trailer parts websites too.
Be very careful, the trailer needs to be strong with enough extra strength to handle cyclic loads without fatigue failures. A fatigue fracture is a sudden break with little or no warning.