You can grow basil throughout the year in Florida. Shown here are three plants: coleus, basil, more coleus. Both coleus and basil will wilt mid-day in August and September if in full sun. They will also bolt (set flower) much quicker if grown in summer. Yet, they are still planted all over S. Florida year-round.

I planted seeds about a month ago. Yesterday, I transaplanted the seedlings into this handing basket. I used a thick layer of spaghum peat moss to line the basket. I also mixed some rootgel into the soil to aid in moisture retention.

Here, you can see the rootgel on top of the soil...it's not the correct way to use the product, but I had extra in my hand and just sprinkled it on the top of the soil instead of putting it back in the container.
I should mention my coleus and basil looked good all winter. Then in January, we had two windy freezes (weather in the 20's) , and
they died within 48 hours.