If I had to take a shot in the dark, I would say this is Margaret Young in 1880 solely on the basis that she is the only one in Laurel, KY where the birth date fits:
"United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MCZW-B7W : 12 August 2017), Margaret Young in household of Thomas Petman, Magisterial District 1, Laurel, Kentucky, United States; citing enumeration district ED 55, sheet 214D, NARA microfilm publication T9 (Washington, D.C.: National Archives and Records Administration, n.d.), FHL microfilm 1,254,427.
As she was the adopted daughter of Thomas and Elizabeth Petman, I would presume that her parents had passed away by this time. Perhaps her brother Joseph Young is a path to more information.