Elisabetha's birth records (Film #1883190, Item 3, p. 384) show mother as SOPHIE FÄSER.

STUMPP, Grossliebental Revisonliste, #181, p. 585 shows a SOPHIE FÄSER, age 17 (DOB 1798-1799), the daughter of SABINA FÄSER, widow, age 53 (DOB 1762-1763).
Depending on the date of the 1816 census, SOPHIE was born between 1 Jan 1798 and 1 Jan 1799.

St. Petersburg records of Grossliebental 184x deaths (Film #1883192, Item 2, p. 34) show a CATHARINA WAGNER, wife of Franz Wagner, on 12 Oct 1841, age 43 years, from Auzberg, Würtemberg, Germany.
LDS film shows name as Katharina Sophia Wagner.
CATHARINA was born between 13 Oct 1797 and 12 Oct 1798.

Therefore, Katharina Sophia was between 1 JAN 1798 and 12 OCT 1798.