Perfectly doable. I did longhaul with both of my DC as newborns.
Be sure you book the bulkhead seats so you can have the bassinet. When we did baby flights (13 years ago!) BA also had baby bouncer type seats they could strap there if you’ve outgrown the bassinet. It is not nice for anyone if you don’t get these seats. I would schedule flights based on this availability over almost anything else.
You can’t buy a ticket for the baby until born, but you can book your seats and call the airline to add baby after birth. I think we called the airline to book our seats and told them we’d need the baby seat and they may have put a note on our reservation to not move us from the bulkhead.
You can often order ready made baby milk to pick up airside so you don’t have to faff with making up powdered on an airplane. Bring a lot of sterilised bottles for the plane so you don’t have to wash there. Breastfeed if possible because it’s easier. Flight attendants were always lovely about the babies. Stick a tin of powder in your luggage. AI over apartment - you don’t need the space at that age and you don’t want to cook.
I wouldn’t bother with a travel cot. Hotels usually have them if you ask and baby will be small enough to sleep in a pram.
It will not be a big sightseeing holiday - you will be tired, jet lag with babies isn’t especially fun. But if you just go with whatever the baby does (let’s face it, you aren’t sleeping regular hours anyway with a newborn), it’s fine. To properly get over jet lag, it takes about an hour a day. Just don’t have expectations higher than hanging around the pool all day. Get a room with a balcony/patio so you can sit there if you have to take the baby back to the room.
It is doable. I did it with two babies with no regrets. Key things are very low expectations, a lot of prep work, and a go with the flow attitude. If you like a lot of control or routines, it will NOT be fun. But if you just want to sit in the sun or by a pool whenever the baby is agreeable, it’ll be fine.