Her death certificate, scanned online at the Missouri State Archives, lists Eliza Emeline Downing, widowed, age 83 years 1 month, born 5 Feb 1842 in Illinois, died 5 Mar 1925 in Warrensburg, Johnson Co., Missouri, father Thomas Burkett, his place of birth unknown, maiden name of mother unknown, cause of death bronchial pneumonia, informant Mrs. J. J. Davis, Warrensburg, Mo, burial in Hobson Cemetery.

Mrs. J. J. Davis is her daughter Gertrude.

I cannot find any match for her in the 1850 or 1860 censuses, under either Burkett or Harris, unless she is the Emma E. Burkett who was a daughter of Needham Burkett and his first wife Annis Pruitt:

1850 census of Fayette Co., Illinois, enumerated 12 Sep, lists as family #488:
Needham Burkett, 39, b. N.C.; Julia F., 27, b. Va; Elizabeth M., 20, b. Tenn; William, 18, b. Tenn; Andrew, 14; Martha, 12; Dolly, 10; Mark, 9; Emma E., 7; Annis, 5; Thomas, 3; Francis W. (m), 1. Andrew through Francis born in Illinois. The gender for Francis does not match the 1860 census.

Fayette Co., Illinois marriage records list the marriage on 16 Apr 1846 of Needham Burkett and Julia Franklin Pryor, so only the two youngest are her children. The others are children of Annis Pruitt or Pruett, whom he married in Tennessee about 1830.

1860 census of Newton Co., Missouri, Van Buren township, enumerated 14 Aug, lists on p. 175 as family #1179/1206:
Needham Burket, 52, farmer, b. N.C.; Julia, 39, b. Va; Thomas, 14; Frances (f), 12; Needham, 9; Jane, 7; Arena, 5; Lear (f), 3; Rosey, 2, b. Mo; Ellis, 11/12, b. Mo. Thomas through Lear born in Illinois.