T.G.
After reading a post about why babies should be secured in their car seat while flying, I wouldn't ever fly again without my infant having their own seat. With that being said, toys that attach to the car seat handle are great. I would keep the baby in the carrier as long as possible because once they are out, they won't want to be strapped back in.
I would pick up a few new things before the trip that you save until on the plane. Make sure you have security items your baby uses (favorite blanket, binkie, toy). A blanket can be used for a game of "peek a boo" or "hide the object". If your child is teething, a dose of tylenol before the trip, teething ring and teething cream/tablets. Bring baby's favorite juice and finger foods like cheerios, gerber puffs etc.
With new FAA regulations, I would go online to your airlines webpage and look up the guideline to what you can or can not take on the plane. Knowing ahead will relieve stress and prevent delays when you get to the airport. Most airlines allow 1 carry on per ticket purchased, but it has to be under certain dimensions.
Good luck and have fun on your trip