Just to add a data point on this (or 14 as it turns out). We've had 7 return trips MEL-MCY with our now 2+ year old child, spread out pretty evenly from when he was 4 months old. We fly exclusively with VA. Up until he turned 2 we flew J as he sat on one of our laps, and on our most recent trip he'd just turned 2, and not being able to justify the cost of 3x J seats we flew Y up and Y+ back.
On all of those J flights the crew were great looking after us, for example being more then happy to stagger our meals, letting us eat in a spare seat so as not to wake bub, or entertaining him if they had a spare moment. To be fair, being in J I took for granted that they'd provided this service.
However it was our most recent trip in Y/Y+ where the staff were most impressive. Being his first flight in his own seat, he wasn't taking to having to wear a seat-belt, so the staff located an infant seat-belt and we were able to secure him on my lap for take off. On descent however all hell broke lose and he wasn't having a bar of the seat-belt. One of the crew came and spoke to him and cheered him up a bit, and then went off and returned with an activity pack to occupy him which worked a treat. On the return leg a crew member came with a container of toys she takes with her on all her flights and spent time sharing them around with the kids on the flight including ours. So in my experience all of my experiences travelling with kids on VA have been overwhelmingly positive.
In terms of kids/babies being disruptive on flights, in my memory there have been 2 times I've been woken/unable to fall asleep on a flight due to the behaviour of passengers. One was in Y+ when the parents of a family of 4 next to us decided sometime after midnight would be a great time to break open the board-game Trouble (the one where you pop the dome with the dice inside) - the crew eventually put a stop to this. The other was in F travelling from JFK-LHR when the portly gentleman seated behind kindly snored/snorted all the way from levelling out through to descent. Not much the crew could do about that!