Slim:
For Louisiana, you are not required to have trailer brakes unless the gross weight exceeds 3,000 lbs. I am a believer in trailer brakes for any trailer over 2,000 lbs., but usually a good set of brakes on one axle will work pretty well.
However, the law in most states says that once you get over the weight limit, all axles must have working brakes. So if you have a tandem axle trailer, you usually will need brakes on both axles to meet the law.