It sounds like what you are wanting to do is fly down and trying to figure is if it cheeper to keep the car for the entire trip or just get it for the way back. The answer is, it depends. I think you have 3 options, and may need to use two of them (2-3 to get the cheapest rate) and you can get the price for each option from the car rental website.
1st option: From when you get there until you drop it back in NJ-10 days
2nd option: For just the time it will take you to drive back from FLA to NJ. At least 1-2 days depending on how long you plan on taking to get back
3rd option: This will mean 2 rentals (option 2 and this one) Get the price for just the days you need it in FLA. Return this option it the day you leave and pick up the second rental, option 2.
Option 1 is probably the most expensive. It will most likely be a lot cheaper to do either option 2 or 3 or a combo of 2 and 3.
If you don't need a car while in FLA option 2 is probably your best bet.
Again, you will have to check as one way rentals are usually a lot more expensive, but sometimes the agancies run deals.
I hope I made sense.