According to the certified flight instructor (CFI), they were practicing touch and go landings. During the second touch and go, the airplane hit a deer, just as the airplane rotated. The CFI continued with the takeoff and established that there were no vibrations and that the airplane was controllable. The CFI elected to divert to a nearby airport where emergency services were available, and landed without further incident. Examination of the airplane revealed that the right wing strut and right gear mount were bent and the right side of the fuselage was buckled.