Airports vary hugely in the facilities they offer to small children.
One of the best is Changi Airport, where there is a Mother's Room as well as Day Rooms. Others seem to struggle to provide as much as a drinks machine to transit passengers. At any sizeable airport you are likely to be faced with long walks to and from departure and arrival gates. Make the most of these if your child is full of energy, but plan for the alternative. Ask for 'special assistance' when booking your tickets.