The "E" tire can carry a heavier load IF it is inflated to a higher psi. If you don't plan to do that, or if your wheels max inflation is only in the "D" range anyway, you don't gain anything. If your trailer came with D load tires, I suspect the wheels were selected to match and have a 65 psi limit. If so, that's the most you can use in the tires and the E gains you nothing. You would need to upgrade the wheels as well as the tires.
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You should consider the axle weight ratings (GAWR) and try to make sure the combined load capacity of the two tires on each axle exceed the max axle rating. For example, if you have two 3500 lb axles, the tires on each need to be able to carry more than 1750 lbs each. A 225/75R15D is rated for about 2540 lbs each, so that would be fine and you don't need a bigger tire. But if the axles are 5000 lbs each, then the d rated tire is marginal, with only 40 lbs of load capacity above what is needed. You can find the axle GAWRs on the federal weight sticker/plate on the left front of the trailer somewhere.
An alternative may be to go to a slightly wider tire and gain capacity that way. Measure the space in the wheel wells, though, to make sure they won't rub.