Hurricanes and dogs
I agree with PDQ. While I wouldn't plan to cruise in the Caribbean during hurricane season, a trip north would make plenty of sense. At some point we all have to take some risks to get the most out of life. For those of us who live north of the Mason/Dixon line, we would miss most of our sailing season if we didn't sail during hurricane season.
If you plan your trip right, with plenty of places to duck into, you should be able to find a reasonably safe spot (at least relative to Savannah) and ride it out in some shelter on land. PDQ is also correct that you usually have reasonably good notice of a risk of a storm. Use caution, but live life.
As for the dog, I wouldn't bring it. I love dogs, and have sailed with our 5.5 lb. Yorkie. The difference is our dog likes to stay inside and is paper trained. It is also very easy to keep her on a leash for her safety, and she would often sit on my wife's lap while we were actually sailing. I really think you are already taking on more responsibility than you are used to, and don't need the added distraction of the dog. Maybe after you have this trip under your belt, you could reconsider whether you want to take your dog on other trips.
If you are absolutely committed to taking the dog, I would start taking weekend (preferably long weekend) trips with the dog to get it adapted to cruising the way you want. Also, look for stories in sailing magazines/websites about people who have traveled with pets. I have read many good ones with good advice. Also, check and see if some pet books have advice on cruising with pets. Cruising books may also be a place to check out. I still think this trip should be about your having fun and having less distraction, but that's just me.
If you want to discuss in more detail, either respond to this or you can PM me. Have a great trip!