Hi over here, Valery. Don't worry, you will get the hang of gardening here soon enough. Tomatoes are grown commercially here in Florida, but as Ann says, it's sort of upside down, and things that grew in summer for you in NJ will now grow winter into spring here. The hot nights of summer don't allow tomatoes to set fruit, and most of them just expire in the heat by about the middle of June.
I know we're all such computer gardeners, but I'd recommend a book for you, 'The Edible Landscape' by Tom McCubbin is all about raising fruit and veggies in Florida. Even though I've gardened here and grown a goodly number of veggies, fruit and flowers of all sorts, I still fall asleep over that book quite often. It's got a wealth of great info on what to grow in your Florida garden, and when to plant, which is critical.
Some cool season crops like broccoli, cabbage and kale do extremely well if planted now. But beware! Since the weather wavers back and forth between toasty and cool from now through February, the cool crops mature very fast, so keep an eye on them. eg. My broccoli goes from perfect to all blooms in about 3 days if it's warm, so you have to be prepared to snatch it and use it.
I help the kids grow a garden at the local elementary school, and we have cherry tomatoes already bearing fruit there. They were planted out as transplants in September. We also have 3 colors of beans already bearing, and we did plant some potatoes, too. Last year we had good success getting a crop of small potatoes, blues, gold and pink ones. The kids think it's a treasure hunt when it's time to dig them. Such fun.
Btw, the secret to getting kids to 'dig in' is to give them a pair of gloves that fit them. It's a magical thing - even the girly girls will dig and pick up bugs to show the teacher, and plant by hand with gloves on.
I used to live in Florida, so I feel free to jump in here. 
Been living in Florida for 45 years but only started "serious" gardening the last three years. Primarily vegetables, but slowly expanding into other areas. Really, just trying to turn our backyard into a relaxing retreat is the goal. A place for myself and my wife to relax and play with her dog while my cat watches jealously from the windows. You all have a nice little corner of the web here and I hope I can add something worthwhile.
