I have traveled a fair bit with my detector, on business trips. So I divide my baggage with one carry on, and one checked bag. I made a foam insert for the carry on
that I put the control head, and electronics into, along with my 10 inch coil. I also put my pinpointer in the carry on bag as well. You can keep your battery in the control box if you like. Then on top of all this I usually put a jacket or other clothing items over top of this to add extra padding. On occasion I have to fly a commuter airline, and they do gate checks of the bags which means they don't go in the overhead with you. (So far everything has survived very well)
You cannot put your digging tools in the carry on, unless you'd like to contribute them to the TSA. I take the lower rods and digging tools etc and put them in my checked bag. My philosophy is to put the things that are easily replaced in my checked bag. Besides my lower rods don't fit in my carry on, unless I were to cut them down a bit, and I see no need to do so. I've attached a picture with how I go about this process, in hopes of inspiring your endeavour. I have gotten a few questions about the contents of the carry on during the xray of the bag, and I just tell them what it is, and that I enjoy the hobby. So far no issues at all with it.
(note this is just flying domestically in the USA)