I travel often with a scooter on an airplane.
You need to notify your airline that you will be bringing your scooter. When you get to the airport, you can check the scooter at the luggage check in and use the wheelchair service to the gate, and then to baggage on the other end, or, you can gate check your scooter at the plane. The check in agents will do the paperwork for you and attach it to your scooter. The gate agents will arrange to have it taken from you at the gate, and taken down to put in the plane...........they then return it to you at the gate on the other end.
We have only had damage once, when going home, which the airline promptly reimbursed us for. We had reported the damage when arriving at the baggage claim, and received a claim check for having it repaired.
Make sure you know how to hook up your scooters wires............as they usually unhook the batteries, and sometimes other stuff. I scanned and printed the assembly/disassembly instructions for my scooter and used a twist tie to attach them to my basket. This has been a HUGE help. I also printed up a list of "beware" items and taped it to the back of the seat.............like "Do not lift scooter by seat, it is NOT attached". Just in case, I look up, on the internet, a medical supplies company at my destination that can repair my brand of scooter if necessary. I've never had to use this information.
You need to know what kind of batteries you have, or have t hat printed in your instructions, so you can show the agents that are filling out your scooter's papers.
It sounds difficult, but it's not, and it's a great help to have it with me. The airlines transport your scooter for no charge, so it is much less expensive than renting one at the other end.