Hope it works. Despite travelling with child, I'd never fly Gulf Air.

The Asian airlines are prety good about children. Due to lots of work, attendants do not babysit, but openly promote children playarea (to avoid kids screaming on long-haul flights) in their galley (as opposed to UAL, for example, who threat with arrest if your kid stays in the galley for more than a minute). Needless to say, they take precautions to avoid accidents.
I have had babysitting on MH and Air China, but it was totally voluntary.
The Qantas nanny-flight attendands (I positively mean more experienced women) are prety well trained to "sense" kid needs while passing by and offer solution beefore kid-burst.
SQ have a personal entertainment on the economy seat, that can keep kid happy for a while.
Both of the above do offer free toys, coloring kits, etc. that might be hidden due to costsavings but still available in the cabins.