Passengers under 18 years of age are not required to have I.D., unless travelling internationally.
As a minor who flies solo a lot, I am usually asked for my ID 25% of the time (100% if carrying medications onboard), but it isn't needed, and if you don't have it, they just ask you to repeat your full legal name (same as on boarding pass), without looking at the boarding pass (lol). Your child will be fine.
Everyone needs a picture id to fly anywhere.
No if with adult companion. If alone, check with airline.
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