Avoid taking toys that jingle or squeak as you have to think of the other passengers and these can be annoying. Take plenty of nappies and small amount's of food for the baby. Most important is to dress the baby in a sleep suit and change before you land to avoid any mishaps, a change of top might be a good idea. Sleep when your baby does.
If the baby travels as a lap child, you would pay just the tax portion of the airfare. You might have room next to you to put the baby, but you might not. You might get stuck holding the baby the whole time, which could be more tiring.
Try to plan in such a way that the baby needs to be fed during take off and possible during landing. Also, try to keep baby up before take off, so child will feel sleepy once you are in the air.
Furthermore make a note of baby travel products so that you would not miss out on any essentials which are required for safe travel and there is some medication which you can bring which will make baby a bit sleepy. But be SURE to check with a licensed doctor though what kind you can take and what the correct dosage is for child's age/weight.
If you pay an infant airfare, which is about 75% off the adult fare, then you can have a seat for the baby and bring along a car seat to strap in. I personally, would suggest this option. It's much safer and easier for you.