You will need to do some math. Look at the sidewall of your current tires for max weight capacity. It will look something like 2500 @ 60 max inflation. Take the Max number times the number of tires. In the example above 2500 x 4 = 10,000 lbs. If your trailer GVWR is less than the total amount you don't need a higher rated tire.
If you do go to a higher rated tire you most likely would not need to run them at maximum pressure. There are tire pressure charts out there from most reputable tire manufacturers so you can match the pressure to the weight of the trailer. This would reduce some of the bounce.