From the age of 13 she was employing tactics and strategy in the field against hugely superior forces, she is an expert in guerrilla warfare and fighter combat. Her training might not be official and she might not have and diplomas to her name, but she'll have learned more about war and battle by the time most of the other characters were old enough to enter Starfleet Academy.
There is also the matter that the station is Bajoran property, Starfleet is just there to administrate as well as observe and assess their suitability to enter the UFP. Part of that agreement is joint working, in "A Time To Stand" she even says to Weyoun, "The Federation and Bajor always shared equal responsibility for station security", and given the number of command, engineering, medical and technical militia staff onboard then I'd assume there was a similar arrangement in place for all facets of station operations.