Non-compete agreements are legal in Florida, but they have to comply with statutory requirements and there is some case law about the scope, in industries, etc. I would take the agreement she has asked you to sign to an employment law attorney for review and advice before agreeing to sign it.
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This is what is called a non-compete clause. They are legal and can be enforced as long as they are not overly broad. In other words they have to have a set time frame, type of job, and location or area. However, if your current employer ceased to exist it is unlikely that anyone would enforce the clause as they are no longer doing business so you are not competing. That being said, you can not be forced to sign this agreement, but you can be terminated for refusing to do so.
Florida is one of the states that enforces covenants not to compete so long as they are reasonably limited in time and scope and do not effectively prevent you from earning a living. The Court can tailor the document to make it reasonable. You need a commercial litigator to deal with any issue concerning this covenant not to compete.