Of course you can. I've been growing veggies since we moved here in 2002.. I usually have broccoli, root veg, salad greens and other goodies right through until April or so. Depends how quickly the weather heats up in the spring. It's too late to plant those now, but right now is the time to plant tomatoes, peppers, eggplant, beans and other things that like the heat. The tomatoes will usually peter out around June, as they don't like the hot nights or humidity too well but just start some more in September.
First question really is "what do you like?". Then start what you like, from seed or transplants - warm weather lovers like tomatoes, peppers, eggplant and beans can go in. Greens, peas, and cabbage-y things like broccoli and cauliflower and root crops like carrots and beets need cool weather so plant those after the first cold front in October, but you can start seeds in September for just about all of them.
I have a favorite book that I fall asleep over all through the fall and winter months. "The Edible Landscape" by Tom McCubbin. It's a great general guide for veggie and fruit in Florida, and also has a page or two about most of the commonly grown vegetables and fruit.
If you want to grow in the ground, you will need to first amend your soil a lot because it's probably pure sand. Find a good source for compost - most counties have a composting program and excellent free compost is available at your landfill. You just have to go get it. Lots of veggie plants are susceptible to nematodes and the more organic material you have in the soil, the less problems you'll have with nematodes. I have such terrible soil, and so many oak tree roots around my house that I have resorted to growing in Earth Boxes. (yes, lured to the Dark Side). But I have grown a lot of veggies in amended beds in the ground up until recently.
