I would get a light weight carseat like others suggested at least as an option. For us, our daughter never slept in her carseat well and I would sleep on my side with her tucked in beside me. I had the seat belt over both of us (mainly it was over me). Was it perfect? No, but I got some sleep and she was comfortable. We always had to hold our daughter at that age to sleep on a plane.
Natural remedies - lavender is about the only option, but it needs to be started as a routine at home. We do use benadryl some, but not until ours got a bit older (over 2). You definitely have to try benadryl at home first.
You are in business class, so it will help, but you might need to bring extra milk. Also, any thing that might distract the kid - even if it is a no go at home like an ipad - bring it. This is a time for (some) rules to go out the window.