The student pilot was conducting her first solo flight, and stated that during the first landing, all three of the landing gear contacted the runway simultaneously, and the airplane began to porpoise. She aborted the landing and noted that the engine sounded "slightly rougher and much louder" during the climb-out. She also noted that the airplane "struggled" to climb to traffic pattern altitude. The second approach and landing was uneventful, and after disembarking the airplane, damage was noted to the propeller. Further examination of the airplane by a Federal Aviation Administration inspector revealed substantial damage to the engine firewall. The pilot reported there were no mechanical malfunctions or anomalies of the airplane that would have precluded normal operation.