Toddlers & babies are allowed to be in bus/first as long as the parents pay for their seats. For safety reason, I personally don't think lap child is good idea esp on long haul flight. If you are getting 2 award seats, it will be 85,000 miles each (same miles for baby). You will call AA to redeem your AA miles for the CX tickets.

Please come prepared (like the web link BettyBoop mentioned) w/ toys, food, and other things that help to keep your child happy and quiet, so the rest of us hopefully can get a good night sleep too. Good luck on your travel plan and since June is the starting busy season for HK, you may want to redeem your AA miles asap.