Hi Melody, just wanted to add that we flew to Australia from the UK when my third daughter was only 7 weeks old. She slept most of the trip, I breastfed her on the plane, and the cabin crew were great, there was a gay guy who took her from me so i could have a break and he was off for half an hour with her showing her to all the stewardesses.
I think you should mention it to your FIL though, if he has to book wouldnt he have to book a skycot at the time as well?

Best of luck whatever you decide xx