"but is it as dangerous as their odd looks are telling me? ... being a woman and sailing alone? "
Forget the woman thing, Poseidon and the other gods aren't going to cut you any more or less slack based on gender. Sailing alone is inherently more risky than sailing with more hands, simply because, well, you're alone! If you fall overboard, there's no one to notice. If the boom cracks you on the noggin, there's no one to fetch help. Is that dangerous? Well, compared to what?
I'd call it a personal choice and as long as you're comfortable with it, that's your decision to make. And enjoy.
The NJ shore can be a rough place in bad wx, if the wind or seas are coming in and you're in the shoal areas, the water can be much rougher than you think, so give it due respect. On the bright side, there haven't been any reports of piracy off NJ for many years now.
<> Very gently! The best thing it to do a mental run-through of the docking process before you even leave the dock. Then on the way in, while you are still in free water, lay out whatever you will need so that when you do get near the dock, it is all at hand. You'll need to keep enough way on so you don't lose control, but I've never been ashamed to come in dead slow, even painfully slow, rather than go CRUNCH. The phrase is "with all deliberate speed", i.e. as fast as you can SAFELY handle it, there's simply no reason to rush, ever, for anyone.
If you'd rather get some practice in private, you can take a 2x4 or stick of PVC pipe (capped at both ends) out to an isolated spot, throw it overboard, and use it as your "practice dock". Nothing much to hit, no audience to applaude, and when you've gotten the hang of it, just pull it back on deck and take it home. (A mooring whip or other stick will help you get it back again.) A "lunch hook" or any simple weight will keep it anchored well enough for what you need to do, so the current doesn't move it and you both.
For safety solo, I'd suggest wearing a PFD (as a courtesy to the SAR folks who can't go home until they locate you) and once you get near 4PM, having a personal strobe or other bright light on it as well, since that's close enough to need one if you go over and no one notices for a couple more hours. A handheld VHF in the cockpit, a cell phone in a ziplock bag or EWA pouch...and if you don't file a float plan, at least leave a note on your dashboard that says "Gone sailing...overdue by 9PM" if you're parked someplace reasonably secure. If you're sailing from someplace with a dockmaster, etc. then giving them the float plan and dropping off the occasional cold beverages is another good way to do it.