6 months is a good age to take a baby. Your baby could be entitled to its own hand luggage, who are you flying with/
we flew long haul with our son at 6 months, he was the perfect size for the skycot/bassinet, i'd advise booking one of these.
a) you need to take at least 1 change of clothes a few toys but nothing bulky, a favourite blanket, make sure baby is wearing comfy clothes, we put ours in a sleepsuit, and took 3 spares which we needed a couple of. take a bottle of water for baby tod rink during take off and landing and during the flight as it really dehydrates them. You'll fit it all in, you're allowed a large carryon bag yourself plus your own handbag with most airlines. plenty of room, the blanket doesn't have to fit in the bag.
b) You sterlise before you go and fill the bottles with water ready, i took a milk powder dispenser and spare water in those thermos flask. I was asked to taste the water to make sure there was no poison in in.
I did try and take a couple of cartons through security but they were taken off me because i wasn't willing to open them to taste them, mainly becaus ei knew that they recommend they're drunk within an hour of opening. powder and water is a much better option. Take a couple of extra bottles too, to allow for delays. You can buy cartons once through security which you can call and reserve the day before you fly, although they may not have your brand. there is normally a Boots store through security.
c) all the nappies you need won't take up loads of room. lets think 24 hours or so, should need say 10-15, i'd buy the biggest hand luggage bag you're allowed. i'm guessing for such a long flight the make allowances for babies, check the airine website and don't be afraid to call them for advice. I called Virgin loads of times before travelling wiht our DS.
don't panic, stay calm, and remember its only 24 hours and you will land eventually. I'd suggest borrowing or buying a baby carrier to free up your hands. are you flying alone of is there another adult with you? i've found a cheap 2nd hand carrier for our next trip with our 2 yr old and 1 yr old.
Hope that helps