This is the RULE:
Flights within the United States
An infant under 2 years of age can travel with you free of charge if held in your lap. No more than 2 infants can be held per row of seats. Contact Reservations and ask them to note on your reservation that you will be traveling with an infant.

If a seat next to you is available, you can use it for your child as long as you put her in an FAA-approved child restraint. If you want to be sure a seat is available, you'll need to purchase a ticket. (For more information on FAA-approved child restraints, see Infant & Child Seating.)

Children ages 2 and older must have a seat and pay a standard fare.

Flights Between the United States and Other Countries
All children, regardless of age, must have a ticket. The price of the ticket depends on the age of the child. For infants under the age of 2 and held in the adult's lap, the cost is usually about 10% of the adult fare plus any international taxes that apply. If you choose to purchase a seat, or if the child is 2 and older but under the age of 12, a discount off the standard adult fare may be offered. In some cases, no child discount is available. For more help, contact Reservations.

SkyMiles Mileage Credit
Infants under age 2 must be in a paid seat to accumulate mileage.

Your child is "2" if you mention this on the BA forum they will slaughter you for STEALING because that is what you are doing if you try to take a child on a plane without a paid ticket if they are 2 years old or older. Next if your child has a paid ticket and is eligible for an upgrade or you purchase an upgrade then you can place the child in a car seat if FC in the seat upgraded to. I personally have three children and I have disgust for parents who hold their children in their laps on any moving transportation! Children in their parents care deserve to have safety and that is only provided by caring parents. Unfortunately there are a lot that either do not have the care or intellegence to do so. For that reason we have to have laws to make them put their children in car seats and buckle up. When a child is an adult the responsibility is then theirs. But until then it is yours! If you child crys a lot, proceed to the restroom and take care of the child. If your child has not flown a lot then pressurization changes could result in ear pain. DO NOT use ear plugs it will make it worse. So to answer your question if I did not do it very well. Your child is 2, buy your child a ticket, then upgrade it as required or sit in coach or consider grandparents. I have 3 children so this is from experience and all of the comments that may come about not liking children are false. I have many adults that are much more undesirable than children. The child's behavior is a result of their parents discipline.