I concur with above suggestions having flown with children at ages from 12 months to 4 years of age in B777s, BAe146s and other large commercial aircraft as well as in the back of Cessna 172s and Robin Dr400s etc.
Use the car seats that are designed to secure via either a lap-strap or lap and shoulder strap. These can be firmly attached to either a light aircraft or a commercial passenger aircraft seat. Once the little critter is secured within the car seat they should not be able to undo either the aircraft seat straps, as they are out of reach, or the car-seat straps which are designed to be difficult for infants to operate.
Hearing protection is essential in light aircraft - get the smaller sized onces supplied by Transair if you can as these will fit a child's head better and give better attenuation or use the existing aeroplane headsets. When flying in the C172 my 2 1/2 year old boy sat in the back seat with a full-size headset on, although it was not ideal as it did not grip his head as well as it would on an adult. During the outward journey he was mesmerised listening to the RT and looking out of the window. On the return leg he fell fast asleep and only awoke when the engine was shutdown and it all went quiet!