Safety of lap infant vs car seat?

I’m flying with my 6 month old in a few weeks and am struggling with whether to carry her as a lap infant or buy her a seat and put her in the car seat. I am willing to spend the extra money if it is truly safer. If the actual risks of lap infant are minuscule I would not want to spend the extra money just for the sake of easing my anxiety. I know there are some convenience benefits to the car seat like not having to hold baby the whole flight, but I’m only asking from a safety POV not considering convenience.

My question for pilots is: what would you do if it were your baby?