I will confess that I am not familiar with the legalities of where on can have a handgun in Florida without a CCW permit. If you plan on doing any future travel at all, I would strongly urge you to get one. It will allow you to carry in 30+ states, including the 16 or so that allow Constitutional carry.
I have flown out of Newark many times with a handgun, and have never had a problem, although the exact procedures seem to be different every time. Follow the guidelines, which have been amply documented elsewhere (or feel free to pm me), and whatever you do, don't say, "I have a gun." Just tell them, "I need a firearms declaration card." I would suggest that you lock your slide back, or even take it off, so they can clearly see that your gun is unloaded. Once you've done it a few times, you will feel a lot more comfortable.
As for defensive ammo, consider a polymer-tipped round like Hornady Critical Defense, which the NJSP has ruled is not a hollow point.
Good luck, and have a good, safe trip.