I will be flying Jet Blue with my 9 month old in my lap. However, I have heard that if you bring your carseat and there is extra room they will allow your child to use it free of charge. Does anyone know Jet Blue allows this or should I just check the car seat?

You may check in a car seat free of charge and will not be counted against your checked baggage allowance. Most taking a car seat will check it in since the car seats will not fit in an overhead bin or under the seat. So, to answer your question, no they won't let you take your car seat on board in the hopes that a seat will be free. However, stranger things have happened but it best to be on the side of caution and not have to pay a one way fare.