Hi ladyjan ... most airlines will carry a baby's buggy free of charge, but perhaps not a travel cot. If you have a particular airline in mind, you would be best checking their website, or asking in the dedicated Q&As topic for that airline here in this forum.

David

Or buy a travel cot which fits in your luggage. Littlelife do them and they are excellent - they pack very small and only weigh about 2kg, so don't use much of your luggage allowance.
If you already have a large travel cot the airline may take it as excess baggage, simply hand it in at check in and pay your dues - but at around £4 a kilo it may not be cheap.

I have taken a travel cot twice. It was a big mammas and pappas one. You tell them at check in, they label it up and tell you to take it to a separate area where they screen it and send it down for you. I have never paid extra to take it

We flew from Manchester with BMIBaby both times.
Hope this helps you.