Agree with wearing harem pants, t-shirt, jacket and scarf. I was given a lovely cashmere cape as a present which folds down like a very small blanket but acts as a great layer when it gets cold on the plane. Probably a ridiculous luxury if this is a one off journey, but as a fairly frequent long haul flier it is one if the best gifts I've ever received!
Don't forget your sunglasses in your hand luggage and an extra pair of socks to put on once you take off. I would recommend comfortable slip on shoes (ballet flats/ skater shoes etc) that you can wear with pop socks (I know!) at the start of your journey and without anything once you are in Singapore/ Australia in the heat - if you want to sleep with them off you won't want to be faffing around tying shoe laces every time you need to go to the loo (and let's face it, you'll definitely be wanting shoes on your feet then).
As others have said, load up on the moisturiser, lip balm, toothpaste and hand cream, and be cautious about what jewellery you are wearing - I have spent uncomfortable hours with earring studs pressed into my neck courtesy of falling asleep with earphones on... I tend to take my earrings off, but then I don't wear anything too precious that I would be devastated to lose if I dropped one. I tie hair back to start and finish, and sleep with it loose.
Remember to drink LOADS of water, long plane journeys are horribly dehydrating, and have a great time in Australia. 