Hi Downgraded,
This is a subject close to my heart! I actually think the choice of airline is less important than whether the timings, routing and aircraft type meet your requirements. On top of that having a solid plan for entertaining and settling the child is essential.
When we bought our two year old over from the UK last year we flew Malaysian to KL, they were actually very good and have the distinct advantage that their loadings were quite light due to the recent issues that airline had.
It is absolutely essential to buy yourself an extra seat. The extra space it provides is tremendous and allowed us to take a whole group of three seats on the A380 (and four on the a330 from KL because no one would willingly sit next to us!). The additional cost may make you wince at first, but believe me when your settled into your seats you'll consider it the best investment you've made all year.
I would say the choice of timing of your flights depends on your specific child and your tolerance to stress. In our case we went for a midday departure because that allowed our toddler to settle in to the environment and eventually sleep come 'night time'. Keeping her up for a night departure on a previous trip resulted in an overstimulated child who would not/could not sleep and became very challenging to deal with - but every child is different.
I would recommend breaking the trip as well if you can because it is unlikely you will get much sleep on your first leg. KL is great for this as it has the cheapest five star hotels in the world.
One more thing - my wife prepared about thirty little wrapped 'presents' each with a little game in to entertain her. Things like crayons, stickers, poms poms to stuff into bottles - that sort of stuff. Each of those kept her entertained for ten - fifteen minutes unwrapping and then playing with the contents - it all adds up.
Anyway - good luck!