Brakes on a Dolly or trailer are important not only for additional stopping power, brakes also keep the trailer behind the tow vehicle. (think JackKnife). When you apply brakes on tow vehicle, the tow vehicle slows, or stops, trailer still needs to shed its momentum. Without brakes it will attempt to keep going either directly into the tow hitch or if at an angle around the tow vehicle.
Also, trailer brakes help stop sway when applied, should it occurs.