Buy your infant a seat
With a 3.5 month old, I'd take the car seat onto the aircraft - it basically doubles as your bassinet at this point.
Alternatively, don't take the car seat onto the aircraft, and make arrangements for the other side: i.e. rental car company provides the car seat, or you check yours in. If you do this, check your stroller as well and Bjorn your little one all the way to the aircraft. For the flight: