I am in the United States. I do not know the word, carrycot. Do you mean 'carryout'? Carryout means food that is bought at a restaurant but carried away. The food is usually in a paper bag.

I'm a US native speaker. I've never heard the word before. Merriam-Webster includes it, but calls it "British." I'm not sure if there's any close US equivalent. There are "car seats," which let babies ride safely in cars. They are made of very strong plastic because they are intended to provide crash protection. They mount in the car facing backwards. Many of them are detachable. The parents can take the whole seat out of the car and carry it around by a handle, without taking the baby out of the seat.