Coopers Hawk

I'm pretty sure that it's a Cooper's hawk due to the contrast of the dark crown and paler nape (most evident in third pic) along with what seems to be a larger bill. Additionally, it is a bit early for sharp-shinned to appear in Florida.

This bird could be either of two species that are notoriously difficult to separate: Sharp-shinned Hawk or Cooper's Hawk. Based upon your report of the size, plus the shape, size and color of the head, I would lean toward the Sharp-shinned Hawk (Accipiter striatus), however the position of the eyes on the head suggests that it could be the Cooper's Hawk. Here is a handy reference to distinguish the species: http://feederwatch.org/learn/tricky-bird-ids/coopers-hawk-and-sharp-shinned-hawk/

Probably a Cooper's Hawk, but just might be Sharp-shinned.