You have to look at New Jersey's CCW laws, and see which states they have reciprocity with. But a quick lookup shows that New Jersey does NOT recognize Florida. It shows:
New Jersey ID, IN, KY, MI, MT, UT
Also, you need to check, because many states have listed that if you are FROM that state, you must have THEIR CCW permit and can't go around their rules by getting a different states. The reciprocity rule is if those residents are visiting your state or you are visiting those other states. So basically, no you can't be FROM New Jersey, get a Florida CCW permit, and use that in New Jersey as a resident. But you need to look up New Jersey's rules.