Hmmm...where to begin? First...you can do this and while your timing is tight, it is not out of the question. We've left the Chesapeake as late as 11/15 and been fine...but cold!
CHARTS & INFO NEEDED
Maptech chart kits for the East Coast
Explorer Chart Kits for the Near Bahamas and Exumas
Skipper Bob's Guide to Anchorages on the ICW
Dodge Guide to Abacos and Pavlidas guide to Bahamas.
Dodge Guide to SE US inlets is also most helpful if you need or want to skip a section of the ICW.
You also need to visit the BOAT US forums section called EAST COAST ALERTS for the latest info on shoaling and dredging etc. once you get your charts so you can mark them up. Skipper Bobs site and the SaltySoutheast cruisers forum has a lot of info too. Don't skip this step or you WILL be aground somewhere! NEVER follow the line in your chart plotter map in the ICW! Eyeballs and depth sounder only!!
Buy a towing policy from Boatus or Seatow.
LOTS of fuel filters (suggest six!) and learn how to change them and bleed your engine before you leave. They will clog at the worst moments.
Have a head rebuild kit as well. Think about an epirb...liferaft is probably overkill if you have a decent dink and leave in good weather to cross the stream. VHF radio is good operating condition is a must and a portable shortwave with SSB band is helpful. Entry fee to the Bahamas is $150 for your boat. You will need a US Customs decal ($25) for return to the USA AND passports.
Down the East River and over to Sandy Hook NJ to await good offshore weather. First night Manasquan inlet. Second night Atlantic City. Third night Cape May...and if your mast is 55' or less you can go out the back way and up the Delaware Bay to the C&D Canal for the forth night. Days 5-8 spend working down the Chesapeake Bay to Norfolk...lots of different choices here for anchorages.
ICW starts at Norfolk...figure 3 weeks minimum to south Florida and more likely 4 weeks from this point.
With good gulfstream weather you can cross over and be in the Abacos or Exumas in 10 hours...but you may need to wait up to 2 weeks to get that good weather.
Do an advanced search with keyword Bahamas and my screen name and it will bring you a bunch of threads on crossing and the Bahamas. Everything else noted above can be googled but if you can't find something...give a yell. You are gonna never want to come back!