Let's not forget that Kira was a rather prominent member of the famous Shakaar resistance cell. Since most of the Bajoran Militia are composed of ex-resistance fighters, plus Shakaar putting in a friendly word (perhaps), plus Kira being a rather sharp, quick-witted woman all easily explain why she was a major in the recently formed militia at age 26.
And as luck would have it (writers <cough> <cough>) she was assigned to DS9.