There are more reasons not to do it than there are to do it. I don't know your sailing skills, but the first thing to tip me off that this is a bad idea is that you plan to do it with one boat. That's bad enough, but your boat is a 16! It is not designed to carry the provisions you'll need. I know you're thinking of sailing maybe 20 miles a day, which isn't much. You're probably also thinking that a catamaran would be ideal since you could go ashore and camp anywhere there's a beach. You're probably also thinking that you'll have a radio or cell phone, lots of local contacts, and a credit card as support. Also, you don't have any responsibilities and no one depending on your support, so you don't have much to lose. Those are the good points.

Have you also thought about what could go wrong and how you'd get out of it? There is no convenient time for something to go wrong while on the water. What will it take to rescue you? What sort of emergency provisions and replacement parts will you take? What about food, clothing, camping gear? How with these provisions affect the boat's performance and therefore your assessment of what it will take to complete the trip? How are you getting back? How will/won't the Coast Guard help?

Here's a better idea - make the trip with someone with a larger boat and more experience and learn first hand what it takes to make the trip. Another idea is to create a flotilla of cats (at least three boats) with a support boat (one with a motor and preferably 25 feet long) carrying the extra gear you'll need.

Your idea sounds like a fun adventure, but it will behoove you to make a better plan.