Spend the money to hire an attorney to evict her. I don't see why she will be there until Mid-February if given notice now. Serve a three day notice then after the time expires you file an eviction action in county court. If she has not paid any money by the sixth business day after she is served you can probably get her evicted. If everything goes smoothly she may be out in three weeks.
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Florida has created eviction laws/statutes to deal with all manners of non-payment of rent in exchange for use of real property.
Self help or taking action outside of eviction such as changing the locks or removing the person physically could provide the renter with a legal high ground they do not have now and potentially cause you to be liable to them. As has been mentioned above, an attorney can potentially resolve this issue in a month's time if the matter proceeds smoothly. Consider consulting with a local attorney in this matter.
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