Will you have your baby on your lap during the car ride to the airport?
No!

Whilst on the plane, will you use the the seat belt when asked to do so?
Definitely!

So book a seat for your 10 month old. Then carry the baby's car seat so he too can be strapped in safely. This will protect the baby in case of turbulence. Left on your lap, the baby might as well be your airbag.