There was a similar thread recently as well: How to earn miles from child fare

You should be able to retro-claim for the last six months, twelve may be too long ago. As long as the kid is in a paid seat, and not on the lap, you can earn the miles. And at least going forward just sign them up and put their miles number.

I would point out that BA makes household redemptions easier, as you can merge together miles from a family, however that would need other family members to contribute too to get to a reasonable number. As such, AsiaMiles may be easier if you are going to be based in Greater China - as you are more likely to earn more on CX in the future.