I fly a lot. I mean a lot. I don't ever carry into an airport and pack it away before I even get there. One time forgetting to have it packed before getting to the counter and you will have more trouble than you can ever imagine from TSA.
The attention at any airport even in open carry states is not worth getting on the no fly list or the watch list or having an airline counter agent stop you from getting on your flight and you having to replan your trip for later connections. It will ruin your day quick. There are just too many gunphobics. While it is a right to open carry at times the attention is going to drive the phobics to get laws passed that make it hard to even conceal carry. Please consider packing it before you leave your car.