Like others - we transport ours. And, from experience, I can tell you that the airlines do have back-ups available in case yours gets lost/delayed. They lost our seat on a recent trip and provided a lender until they delivered it to us. Like others have said, car seats and strollers are considered 'accessibility' items like wheelchairs and are transported at no cost.
My only added FYI - unless things have changed, you will not be able to use the resort baggage service if you bring a car seat. We had a rental car for a trip, but wanted to check our bags at the resort to save the hassle when we returned to the airport. They told us they couldn't handle the free baggage issue with the car seat and would have to charge us as though it was an extra bag. Don't understand why this is an issue, but we ended up having to check everything in ourselves at the airport.