The Eastern Cottontail rabbit is common in Florida. It is grayish brown with a white tail. It is about 14 to 17 inches long, weighing about two to four pounds. The Cottontail is an herbivore and eats grass, weeds, flowers, and gardens. Yes, rabbits have predators including bobcats. The rabbit you see today might be supper for the bobcat, coyote, or hawks.
There is an interesting Suntree story of a few years back told by George Rosenfield, longtime Suntree resident and environmentalist. A bobcat got into the Brevard Zoo and ate some birds, so several bobcats were rounded up and taken to the Enchanted Forest Sanctuary in Titusville. The next year there were so many squirrels and rabbits in Suntree that George called Animal Control to ask what was happening. He was told the bobcats were removed. He said, “Well, bring them back.” Once the bobcats were back, the balance in our ecosystem was restored. Hundred Acre Hollows is important for the many animals that live there.

Source: http://myfwc.com/wildlifehabitats/profiles/mammals/land/rabbit/