I too have Chinese tires on my trailer - they came from the factory. Suspect the size is the same as yours: ST185/80D13, load range D.
No catastrophic failure from these. They are now 5 years old. Wear is less than stellar.
Add to the spotty track record of Chinese tires the fact that these barely are capable of my trailer's weight, by definition of "ST" speed limited to 65 mph, and are bias ply, I sought an alternative. This alternative is my project this spring as some work for me is required to fit the new tires.
My search lead my to looking for the smallest LT tires, the only other designation suitable for trailer use. LT I learned generally doesn't come in anything smaller than 15". Not going to work. But more digging revealed LT tires are also known as "commercial van" tires in Europe. I found 185R14C load range D is the smallest size available in North America. Diameter overall about 1" larger than what they will be replacing, so doable.
Once done, I will have Q rated (100 mph) radials with room to spare in load capacity. In my case, besides new wheels, some mods required: axle height and trimming excess metal from the wheel wells.
You can find this size from a few brands: Continental, Vredestein, Yokohama and Nokian. I am looking at the Continental Vanco 2 myself.