Im a flight attendant so I may have some answers for you. Some aircraft unfortunately don't have a closet on board. I'm not familiar with jet blue but it sounds like thats the case on them. It doesn't mean though that you cannot bring it onboard! They are just letting you know that they wont' be able to hang it. If you are carrying it on the plane they just want you to know that it will be considered a carry on item. (The FAA only allows 2 carrry ons per person) So they probably can't make a special exception and let you bring on extra.
They are also letting you know that all carry on items that come onboard have to meet the size requirements and they must fit in the overhead bin. If the garmet bag doesnt fit you cannot have it on your lap, and then there is a problem.
I'm assuming you won't have any problem with your dress since destination dresses are usual small and light on material. If you had a princess Diana dress or something then you might need to consider shipping ; ).
I'm guessing that the airline has dealt with some brides who were caught off guard thinking that they could bring a very large dress on board and I bet the flight attendants felt horrible when there was nothing that they could do! (Trust me if there was something they could do they would!)
I would call the airline just to double check that the specific aircraft that you are scheduled to fly on doesnt have a closet. Most planes have a closet especially if there is a first class.
I know that I personally try my hardest to accomodate all my passengers. Especially those with special items. If there is a closet onboard I would totally put the dress in there and I assume that other flight attendants would do the same! Best of Luck!