They likely will not let you take it on the plane to put in overhead BTW. I've heard that from many parents, that they don't want it on the plane for any reason.
We gate check ours because I'm afraid they'll get lost with the luggage (though we HAVE luggage checked when I'm alone and can't carry the extra baggage to the gate, and been fine). When you check in your luggage, the agent there has huge durable plastic bags. We grab one of those and then when you enter at your gate and the agent welcoming you to the plane will direct you to the proper place to put it (bottom of the stairs or end of the walkway depending on the situation). When the girls were smaller we also gate checked the stroller. They put them on and take them off like they would a wheelchair. It is the last thing stored and the first thing taken out, it will be wiating for you a the bottom of the stairs or front of the walkway when you get off the plane.