A good resource for Georgia history is the "Georgia Room" in the Live Oak Library system, Bull St. branch, Savannah, Ga. www.liveoakpl.org.
Avian Mclain,age 27 born Georgia, appears in the US Censu 1880 residing with her siser, Susan Mclain, age 38, born Georga, at Skull Shoals, Greene County, Georgia Avian was born 1852/1853. Avian was single in 1880 and worked in cotton mills. Avian's mother/father were all born in Georgia.
There were only two girls born into B. H. McClain's, the father household recited in the US Census 1850, Susan above, and AMY McClain, age 5 years. Probably your Avian is AMY. The birth dates as calculated are 1845 and 1853 so the indicators are in line.