Actually, just like in a car, a baby or toddler is much safer strapped into an appropriate car-seat that is belted into the seat. Plane seats and seatbelts are designed for adults, so are not very safe for young kids in a crash. It's been shown that babies who sit on their mothers lap have a much higher risk or injury or death in crash or heavy turbulence. It's fine to hold them for feeding or to quiet them, but they are safest in their own seat.
To be honest - a car seat is probably much more comfy that most plane seats - and a sense of the familiar might help to calm a kid who is flying for the first time.
Most babies are carried 'in lap' because it's cheaper and it can be a pain to carry around a car seat. But that doesn't make it safer or make it wrong to use a car seat.
You should check with the airline because some airlines only permit certain 'approved' brands or types of car seats.