As other posters have recommended, try and get the seat at the front of the cabin with the bassinet (sp), you may actually be forced to take this seat by the airline.
This has two big advantages, 1st it gives your baby somewhere to sleep. Secondly, passengers with babies will normally be given priority for those seats and the airline may even bump another passenger out of them. Any passenger with half a brain will avoid that whole area when checking in if they cant stand crying babies. If they choose not to, then it's their own fault for being dumb or checking in late. Either way you have no reason to feel guilty if your little one does not settle. Naturally you'll always get the odd gimp that books a sest next to the bassinets because of the extra leg room, only to look horrified when someone with a baby sits next to them. But you cant plan for dumb-assery.
I've travelled quite extensively in business class with BA, Brunei Airlines, Air France and Singapore Airlines. A business class ticket is certaintly no guarantee that there will not be small children. I've only been in First once (free upgrade) and there was indeed a Baby in the cabin, this was with Air France. The only way therefore to absolutely guarantee a child free flight is to either charter a private plane or book all the seats on the flight. Alternativelty just chill, get some good ear plugs, drink a few beers and relax.