I've taken Guitars with me on planes like 3 or 4 times(on international Flights), and they allowed me to take the guitar right in onto the plane and put it in the storage compartment(although It probably depends on the size of the plane). I used a hard case for my acoustic and my guitar was fine.

Although I would advise you to Detune the Guitar strings until they are very loose, because When you get up in the High Altitude your Strings will snap if they are tuned too tight.