Thank very much, that's very helpful! I am buying Business for my child (hope it should yield the same answer).
I phoned AA, they gave me a totally different answer, they said I need to buy adult fare. However, I haven't had a chance to speak with BA agent, since whenever I am available to call them, it's after their office hour!
I am Gold, so phone fee shouldn't apply.
I am more concern with my experience with AA, they force me to change to child fare when I purchased an adult fare (international itinerary, domestic doesn't matter) for my child for one instance, they forced me to refund the fare difference and reissue the ticket, although they gave me one time exception for not charging a change fee. I will try to phone BA again.

Thanks!