Amazing write up! Haven't even thought about wildlife but man I hope I can see a bear from a safe distance haha. Thanks for the tips!There's some great advice in this thread. I think, even if you don't go with the Willys, you'll still be fine. My JK was a Sport S and I ran it on trails bone stock for about a year before putting any upgrades on. Even a Sport is an extraordinarily capable vehicle. That said, the better tires on the Willys will likely serve you better than the Sport's street tires. And tires are pricy, might cost you less to get it from the factory that way in the long run.
Definitely recommend keeping the Tow/Aux package. Just getting the aux switches alone is super helpful. Makes installing lights or other accessories a total breeze. Plus, you never know if you might want to tow something down the line.
For camping, I usually start by checking public lands. There's not much (if any) BLM land in Florida--not like out West. In which case, I'd recommend checking out your national forests. There's an abundance of trails in Ocala NF, but I can't speak to the Jeep camping situation there (I never got a chance to take my Jeep camping up there, unfortunately.) Check their website and should give more info. There's probably good trails & camping up in Apalachicola & Osceola NF too.
I usually use GaiaGPS and their Public Lands, MVUM (motor vehicle use map), & USFS Roads & Trails overlays to help find trails and places to camp. But always dig deeper to make sure things are still open. Closures happen all the time.
Since you're going with a dog, make sure you check to be sure the areas you're going are dog-friendly, too. Most national forest and BLM land generally is, but national parks are very dog-UN-friendly.
As for camping safety... Florida's kind of hard to get truly off-grid, but there's still a few areas that lack cell service. So, if you're traveling solo, I recommend getting a GPS messenger for emergencies. About 99% of my camping trips are solo and I've been carrying a beacon for years, just in case. Better to have it and not need it than the reverse. Different brands offer different plans. Garmin has a plan where you can pay just for the months you need it, if you don't want to pay yearly.
Also, consider taking a walk-out bag in case you get stuck or break down and have to hoof it back to civilization.
Oh, and be bear aware. Florida bears aren't likely to rip your Jeep open like in the Sierra Nevadas, but they'll still get into your food if you leave it out. Store it all in your Jeep with the hardtop on--food, trash, and anything else they'd be interested in like toothpaste.
You're going to love it. I bought my first Jeep for the exact same reason--to go camping in remote places alone with my dog. And it's been one of the most rewarding experiences ever. Nine years later and I'm on my second Jeep. It's addicting. Welcome to the obsession!