In my state, a parent can ask the court to terminate another parent's parental rights to a child. I just did a quick Google search, and the same appears to be true in Florida.
The Grounds for Termination of Parental Rights statute in Florida is Florida Statutes 39.806. It lists the reasons why a parent's rights can be terminated. Here's the link.
Another site, http://library.adoption.com/articles/grounds-for-termination-of-parental-rights-florida.html
The department, the guardian ad litem, or any person who has knowledge of the facts alleged or who is informed of those facts and believes that they are true, may petition for the termination of parental rights under any of the following circumstances:
It attributes that to section 39.806, but I don't see that language in that particular statute. That language could be in another statute, and the site combined the two to explain things.
At any rate, I'd suggest that you talk to a Florida family law attorney, your local prosecutor, or your local Department of Children and Families office. Here's a link to the Florida DCF branch office finder.
Be prepared, though, that if you approach the prosecutor or the DCF, you might also initially be placed under the microscope. Your best bet is to contact a family law attorney. The Florida Bar Association's Family Law Section has a website that allows you to search for a family law attorney: http://www.familylawfla.org/
If you can't afford to pay an attorney, you should try a local legal aid office. The Florida Legal Services website has information about legal aid offices in Florida. Legal aid organizations do, however, have some income limits. In my experience, though, legal aid organizations will try to help you find an attorney willing to work with you on payment terms, if you don't meet the financial criteria.
Finally, several of the Florida Law Schools have family-law legal clinics. Among them are:
Florida State University: http://www.law.fsu.edu/academic_programs/jd_program/cac/index.html
Florida Coastal http://www.fcsl.edu/clinic/live-client-clinics
University of Florida http://www.law.ufl.edu/centers/childlaw/faculty.shtml
There may be more, so I've included a link to a list of law schools in Florida. http://www.alllaw.com/state_resources/florida/law_schools/
I hope that this helps you to protect your child. Good luck to you.