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Aside from the obvious better solution to have brakes on both axles, I'd put the brakes on the front axle simply because trailers are heavier towards the front to achieve tongue weight.
I thought that would be the response. I bought the trailer in 97 with no brakes. Swapped in an axles with larger hubs & brakes on the one. Only towed within 250 miles for a lot of years. Couple of years ago took the Jeep to Moab, planning on going again in a year or two, going through the mountains I thought the braking could be better. It will have brakes on both axles before the next trip.
JIM.