If you booked a window seat and you have an empty seat next to you, you can put your car seat there without paying (infant ticket in the USA). I’ve done it multiple times with delta and Bh so far it always work. If it’s a full flight you might want to get a window seat in the back and usually the last seats to be taken are the back middle.
We use the doona and it’s been really great. Only thing is that (at least won’t the planes we had with delta) the doona doesn’t fit in the aisle in economy so you have to carry it to your seat