California has a law regarding this:
"California Labor Code § 1030-1033.
2002: Chapter 3.8, Section 1030, Part 3 of Division 2 of the Labor Code
1030. Every employer, including the state and any political subdivision, shall provide a reasonable amount of break time to accommodate an employee desiring to express breast milk for the employee's infant child. The break time shall, if possible, run concurrently with any break time already provided to the employee. Break time for an employee that does not run concurrently with the rest time authorized for the employee by the applicable wage order of the Industrial Welfare Commission shall be unpaid.
1031. The employer shall make reasonable efforts to provide the employee with the use of a room or other location, other than a toilet stall, in close proximity to the employee's work area, for the employee to express milk in private. The room or location may include the place where the employee normally works if it otherwise meets the requirements of this section.
1032. An employer is not required to provide break time under this chapter if to do so would seriously disrupt the operations of the employer."
When my first daughter was born, I worked for a company that is/was very friendly toward women, and they happily provided a locking office right near the kitchen where moms could pump. With my second daughter, I worked for a company where my boss told me, "I guess you don't value your career very much if you decided to have a second child AND now you're asking for somewhere to pump?!" Ultimately, the CA law gives employers wiggle room to get out of having to let you pump with the "if this causes problems for the employer, then never mind" clause at the end... :-/
PS: I know your question was specifically about Florida, but since there are a lot of moms on the site from other places, maybe the above reference can help them...