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I emailed easyjet when I flew with my 10 month old. No you don't pay, and yes you can take it to the gate or steps when you board. They also said that you can get it back at the gate or steps, but this turned out to be untrue, and the air stewards said it never happens. I'm not sure how old your little one is but I would recommend a carrier in your hand luggage for when you get off, through passport control etc.