The student pilot was flying the first leg of a solo cross-country flight. The departure was uneventful, and she requested a stop-and-go landing with air traffic controllers as she approached the first destination. She received the clearance and began to initiate the descent while extending the flaps. During the landing flare the airplane encountered a gust of wind, and she applied forward elevator pressure. The nosewheel struck the ground hard and she attempted to perform a go-around, but the airplane departed to the right of the runway and came to rest in a grass area. The nose gear was bent aft during the initial ground strike, and the airplane sustained substantial damage to the firewall and forward fuselage. The pilot reported no preimpact mechanical malfunctions or failures with the airframe or engine that would have precluded normal operation.