The pilot and pilot-rated passenger of the tailwheel equipped airplane planned to stop at three back country strips before returning to their base airport. The pilot opted not to land at either of the first two planned stops, because she was uncomfortable with the winds at the time of her arrival at each. The third intended destination airport was situated at the shore of a lake. The turf runway was oriented approximately perpendicular to the shoreline, terminated at the shoreline, and was sloped uphill away from the lake. Tall trees and rapidly rising terrain at the other end of the runway resulted in the runway being effectively one way in and one way out, over the lake. The winds were light and variable, and the pilot landed uneventfully at that airstrip. She taxied to the far end, turned around, and began the takeoff roll downhill, towards the lake. She brought the tail up, continued the takeoff roll, and the airplane became prematurely airborne after "rolling over one of the bumpy spots" on the runway. The pilot reported that she tried to fly in ground effect to build airspeed, but lowered the nose too far. The propeller struck the runway, which degraded the airplane performance, and prevented the airplane from successfully climbing. The pilot determined that at that point, she was too far down the runway to safely abort the takeoff on the remaining runway, so she sought a spot straight ahead on the exposed lakebed on which to land the airplane. The pilot steered the airplane towards what appeared to be a dry area that was clear of debris. The airplane struck the dry upslope on the main wheels, and the left main gear impacted a tree stump. The airplane then nosed over to the inverted position. The airplane sustained substantial damage to the wings and fuselage. The pilot reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.