http://www.startpetsittingbusiness.info/

In Florida, just about anyone can obtain a business license just by paying for it...depending upon the business. (Contractors, doctors, for example, do have their own professional licensing departments.)

www.myflorida.gov

You need to check with the State, Counties and Cities you will want to operate within, for their own additional requirements. Some Cities require qualifications, some only require registering at no charge.

You also need to look into being bonded (very expensive), liability insurances, and incorporating (to protect you and your assets personally.)

Good wishes!