The pilot stated that he had completed a touchdown and was on rollout when he noticed a deer on the runway. He increased the power enough to avoid colliding with the deer, but stalled the aircraft and collided with the runway surface, failing the nose gear. The aircraft flipped inverted and skidded off the left side of the paved surface, receiving substantial damage. The pilot and passenger were not injured. The flight departed Lafayette at 1900 hours. The pilot reported during a telephone interview that after the initial climb, he noticed that the aircraft lights were dimming and felt that the flight could not be continued. He stated that the traffic pattern and landing was made without using the landing lights. During the landing roll, the pilot said he saw a deer on the runway. He then proceeded to increase power to go around. The aircraft climbed high enough to avoid a collision with the deer, but settled back to the ground. The nose gear failed and the aircraft flipped over on its back.