There are several different licenses that may or may not be required. First, in order to be compensated for property management in Florida, you will need a sales associates license at a minimum. With the sales associates license, however, you can not operate your own company. You must work under the direct supervision of a broker. After a year working for a broker, you can take the broker pre-licensing class, the state exam, and then open your own brokerage. At that point you would be eligible to operate independently. Typically, however, most agents find that regardless of the license that they have, it is more beneficial to work with an established real estate brokerage. The small offices don't tend to produce the same volume.
Another consideration that you should make is with regards to a CAM (Community Association Manager) license. You will need a CAM license if you intend to manage a building or community with more than 50 units or with a budget in excess of $100,000. There may be other requirements as well so I encourage you to look into it.
Obviously, there are instances where yo would need a CAM license but not a real estate license or vice versa. I hope that helps.