jc, I'm pretty sure you could rent a camper or trailer in Florida. You won't need to sleep on the ground or even use sleeping bags. Most of the bigger campers, and when I say bigger, I mean anything larger than mine. At 13 ft, 3 of which is the trailer frame, there isn't a lot of room for the niceties in life. I've been camping since I was a wee babe. I believe my first foray into the wilds took place when I was just shy of 3 months. I don't suggest you go all native on your first outdoor excursion though.
Whilst I'm on the topic... What the hell do you mean by warmer? I doubt I've ever been camping in your daily mean temps? and yes, I do mean your winter weather. I'm just waiting for the snow to melt before I head out...
Camping can be as elegant or rough as you make it. I tend to cook more gourmet meals over a campfire/stove than I do at home. And there is always copious amounts of red wine, and it may seem silly but I never drink it out anything but a nice wine glass, no plastic here baby....
I've only ever camped south of the border once, but I'm hoping to go again soon. The last time, in California, near Mendicino, we were in a sleeping in a tent with my daughter who was a baby at the time. I awoke to find cat prints in the dust on my car. It wasn't until I was back up on Vancouver Island, and my aunts very fat cat also walked over front hood, that I realized we'd been stalked by a bob cat or a cougar. Both paw prints were still visible and then the size difference was very noticeable.
I'm not all to keen on tents either, thus my new/ancient rig. There is something about escaping the day to day business of the city and living life simply. I love waking up to the silence of the great outdoors, which isn't really silence, not with birds singing or wolves howling...
Camping is also about camaraderie as well.. Meeting people from all over, sharing a beer or a funny story with strangers or a parcel of friends around a campfire. Enjoying nature, the scenery or a fresh caught fish, - I'm allergic but I can see the magic in the moment..
When I was about Antonio's age, I always met new friends at campsites. Other kids who we'd explore with, build forts or very sinkable rafts. We'd go snark hunting or off to look for buried treasures. Or swim all day and then fall a sleep under star covered skies.
Camping can be a miserable experience or make for some of the best memories, but you have to be prepared for the worst. And somehow, even if it pours rain, I always seem to remember the best of it all.
I hope you get a chance to experience it. Talk to some friends and see if they've done it and what advice they can give you, what to bring and where to go. I highly doubt you'll hate it.
If you do go, don't be afraid to ask questions here. I can help you get a list of the must haves. It can be as cheap or as expensive as you want to make it, but whatever happens it won't be a trip you'll soon forget.