that a married lady was needed...

Examples from other JA works would be the Dashwood sisters going with their sister-in-law Fanny to the musical evening and Mrs. Norris (in place of their mother) taking the Bertram sisters out into society. The only exception I can think of is Miss Bates taking Jane Fairfax to the Highbury ball, but perhaps a maiden aunt of a certain age was an equally acceptable person. In fact, I seem to remember JA herself saying that she had reached the age of being a chaperone.