My wife and I have flown multiple times with our 2 kids since they were infants (5 and 2 yo), primarily overseas to Dubai and India. My experience is that emirates and qatar have seemed to be the most helpful and kid friendly, especially in economy. Dubai airport is extremely helpful with complimentary strollers which is a godsend (stroller pickup at the jet bridge is usually painful).
On a side note, we just got back from London on virgin upper class. Not a good way to travel with little ones!! The herringbone (coffin class) is good for single travelers but is very isolating and difficult to see your kids. If your little one is still a little clingy or needs to be observed more often, I strongly recommend another airline for business class.