Call_Bell has it right, there is nothing worse that trying to juggle everything at the same time!!
In my experience watching and helping families with small infants on long flights, the parents seem to forget they are supposed to be having a good time as well.
BA have two types of baby facilities that are available at bulkhead seats. One is a baby cot, so the infant lies down all the time, the other is a type of baby car seat that enables the baby to sit upright or can be tilted so it lies down.
Bring a couple of changes of clothes for the infant, some warm and some cool ones, so you can change it (sorry don't know if it is a boy or a girl), according to the cabin temperature. Don't forget to bring something light you can change into, should the little one have an accident on you.............BA will provide blankets and pillows for the infant, something less to carry.
Don't be afraid to leave your seat and take baby on a stroll around the cabin when the carts are out the way. Most of the cabin crew get real broody over babies and will almost always give you a hand with anything you need.
Ask the crew if you and your partner can eat separately, this allows one of you to look after the baby while the other gets to relax and enjoy the meal, then swap over.
BA crew will not hand hot beverages over children, so why not hang on and have a cuppa when the baby is asleep? Less worry for you as well.
When you first get on the aircraft, as you are sitting at a bulkhead seat, you will need to put everything into the overhead locker for take off and landing. You can have it down during the flight though so don't worry.
During turbulence, the infant must be taken out of the cot/seat and strapped into a seatbelt. Even if it is asleep. Not ideal for you we know, but much safer for the baby. Passengers are also not permitted to sleep on the floor of the aircraft, this includes babies.
That's all I can think of really, apart from have a great time and when you get back, drop us all a line and let us know how you got on.