Looks like she took it legally. You don't have to agree with her methods of taking the animal but gators don't have many natural predators in that area and hunting seasons are necessary.
For those that are real upset about this you should see the show Swamp People.
http://www.history.com/shows/swamp-people these guys fill hundreds of gator tags each year. In one of the episodes they took a huge 12 footer (nothing close to this woman's though).