Not really much to add to the replies on packing, we have a bag and use nappies.
Make sure you stick something in it with your contact details.
I am a fan of the official Gatwick valet parking. The staff are normally fine if you need to do a bit of faffing around with small kids on the drop off. And then it is an easy walk from there to check in. Make sure you use the left hand entrance when you have crossed the terminal forecourt. Someone shared a 20% discount code in the Gatwick thread.
You will need to get the seat tagged at BA check in then take it to the oversize bag drop in the next row to drop it off. They will want to see the matching boarding pass too. The lifts up to security are nearby.
Gatwick has a family security channel, though we tend to use Premium.
If you want a log book for your little one you may need to ask in the log book thread as they are hard to track down on Gatwick flights.
Final tip - leave loads of time and then some more.