The pilot stated that moments after lift-off, the engine began running roughly. At an altitude of about 20 feet, the engine lost power. The pilot stated that the airplane was headed in the direction of a row of trees, so he negotiated a 90 degree left turn to avoid the obstructions. Airspeed dissipated, and the airplane settled to the ground. The landing gear was broken off during ground impact. During an investigation, the propeller was replaced, and an operational check of the engine was performed. The engine operated in accordance with the manufacturer's operating specifications.