We did the same trip in F when our daughter was 3 months old. I would highly recommend doing the A380 LHR-SIN, and that way you will have a few hours in SIN to shower and relax, and then do the 777 leg SIN-SYD. 2/4 flights they ran out of cots, but was a few spare seats, and we brought our own SleepyHead pod (probably my best investment ever, given our daughter has done 12 long hauls). I would concur with CIHY that the "cuddle seats" in Club is actually better for traveling with an infant, since you will have more space to spread out on floor, and using cot in F renders TV useless (blocked). Having said that, for such a long flight, the added luxury of First is actually nice. An added bonus, on the A380, in front of row 1, you have a massive space in front of stairs if the little one wants to move, and nobody is ever there. Any more questions, feel free to PM me for advice, I have plenty to give. Don't forget to get the BA Little Skyflyers booklet and keep track of the flights! :-)