The solo student pilot reported that he made a 40 minute flight to the destination airport in order to meet a family member for lunch. In order to initiate the landing flare, he pulled back on the control yoke, but the airplane's nose pitched up more than he expected. The pilot stated that he corrected for the higher than expected pitch attitude by pushing forward on the yoke, resulting in the airplane's nose wheel being "dropped" onto the runway surface. After contacting the runway surface, the nose wheel porpoised (bounced) one time before contacting the surface a final time. The pilot was ultimately able to stabilize the airplane by applying back pressure to the control yoke. Although he did not become aware of it until he returned to his initial point of departure, the airplane's nose wheel had struck the runway surface with sufficient force to buckle the lower part of the firewall and the forward portion of the floorboard. The propeller had also come in contact with the runway surface. The pilot reported no mechanical failures or malfunctions with the airplane at the time of the accident.