We always bought seats for our children no matter how short the flight. An approved safety seat is the safest place for a 12 months old. I would avoid the bulk head since you may have a long time before the captain turns off the seatbelt sign and you can safely gather your carry on.

I always dislike when families have lap children in first class. You love your baby, but if I'm travelling without my kids, the endless game of peekaboo with your child gets pretty irritating.