We've flown with Virgin to Florida a few times with small children.
My thoughts are that there's no point taking the carseat into the cabin. Firstly, unless you've specifically paid the fare for a seat for your baby there will be no where to put it and secondly, the seat may not actually be safe fastened in an airplane seat - and some airlines do not let you do this.
Unless you've paid for a seat for your baby, they have no luggage allowance beyond the pushchair (and possibly a carseat going in the hold)
Definitely phone the airline to reserve a skycot/bassinet and bulkhead seats. However, you have to take your baby out if there's turbulence which is a pain when they're asleep. Still, it's good to have somewhere to put them so you don't have to hold them all the time.
Don't think there's a restriction on size/weight of pushchair.
Try to feed your baby on takeoff/landing/whenever you feel the pressure in your ears. I mean BF or bottle, not pureed carrot!!
Take a small change bag for your baby as the toilets aren't that big!
Look at your baby's ticket - you should be able to see if it says Infant or "No seat" on it to see if they will be on your lap. If they'll be on your lap, ask at check in if the flight is full. If it's not full, you may be able to get the window and aisle of a set of 3 allocated to you and it's unlikely that the middle seat will be allocated to someone else.
Something like "Medised Infant" cold medicine will make your baby drowsy and is suitable for the under ones. Be careful with Phenergen - I've heard horror stories of it making children hyper after just a short nap if not administered at a genuine nap time (probably more of a problem with an older baby). A friend flew to Oz with 12 month old twins and her GP prescribed something drowsy for them (the twins, not the parents!) so this may be worth trying.
Good luck and have fun!