There are car seats that can be secured solely by the lap belt, without the requirement for an anchor point. My child uses a Radian seat in the car, which has the advantage of being rear facing much longer than a standard seat. I haven’t used it in a plane, but I did a trial fitting in an Archer a few years ago and it would have worked fine. Buying a new seat that doesn’t need an anchor would of course be expensive, but peace of mind and all that. I’d personally never take my daughter up without a proper seat. Like others have said, when they’re young they seem to sleep as soon as the power goes on, waking up as you touch down.