Notwithstanding the coments above which are all quite reasonable, I think you can get the experience you need along the way if you just take your time and do it step by step. You and motor & sail down the Hudson after doing your lake sailing...they do some short day hops in settled weather along the Jersey coast. Then bash up the Delaware and cruise the Chesapeake Bay and get some experience in wider open spaces and squalls. (Also a good place to make repairs ad further outfit your boat as you discover what is needed!). From there you can head down the ICW to Florida and the Keys or make your first "Ocean" passage over to the Bahamas as you feel more comfortable with your skills. Passages south of the Bahamas or out to sea tend to be a bit more challenging (or downright scary) but can be undertaken once you really know your capabilities are up to it.
Go for it...but not all at once!!