how much spare money do you have? Could you afford a seat for DD? Invaluable for us travelling with a 22 mth and nearly 4 yr old.
I second hiring a sling from your local sling library - we took one to HK, and both kids were carried in it. There are less pushchairs and more slings in HK (tho noticeably more pushchairs this time than 5 years ago). They also slept in in during the day and on the plane.
What kit will you need in Singapore? Anything you can borrow (travel cot, car seat - tho check what the rules are like, they just don't use them in HK)
You can buy things over there - we took one pack of nappies, and bought more nappies and wipes over there.
Ask for help - the cabin crew were really helpful. And there is always food / drink about, Ask if there is something specific you'd like and see what they can do - they produced a spare First Class fruit salad when DS1 stropped about breakfast, and I asked if they had any fruit.
Take boiled sweets (even if they don't normally eat them) or a drink in a bottle for take off, and landing.
Take calopl sachets with you on the plane - there is nothing worse than a teething toddler, and nothing you can do about it for 24 hrs.....
Enjoy it!