I got a combo unit which has a wheeled frame that the push chair or car seat fits to. I got a bag mentioned by many to put the lot in, red and marked that it contains a push chair and to handle with care.
Travelled multiple times with it long hual with two changes of planes. Here is home from its last ever trip, KOI-GLA-LHR-SIN-LHR-EDI-KOI.

Oh yes, everything on that truck is mine.