On the one hand, I've never had an issue pulling loaded trailers without brakes on my tow rigs. Both were/are 3/4 ton ext cab LWB dodge rams, though, which makes a big difference - 156" wb, 7000 lb trucks are pretty forgiving.
On the other hand, its illegal to pull those trailers loaded without brakes.
My current setup, I have brakes on both axles, radial tires on both axles, and a prodigy brake control.
As Bones keeps saying, find out what axles are there and see if you can upgrade things.