Family #37 in the 1798 Grimm census.
Family #38 in the 1834 Grimm census.
Sophia Dorothea was from the village of Dobrinka (Nizhnaya Dobrinka). I checked the 1767 census records, and the only Maiers in Dobrinka spelled their name Meier. I've therefore added it as an alternate spelling for her last name at birth.
There were only three Meier families in Dobrinka in 1767. One was a 78-year-old widower, so I have excluded him as being her father just three years later at the age of 81. The other two Meiers are both possibilities.
Johann Georg Meier, 48, Lutheran, a handworker from Mecklenburg, Rostock, and his wife Margaretha, 40. In 1767 they had three children ages 11, 6, and 3. It is definitely a possibility that Margaretha had at least one or two more children, allowing for the birth of Sophia Dorothea around 1770. 
Juergen Meier, 54, Lutheran, a farmer from Darabach, Austria, and his wife Catharina, 40. They had one 10-year-old child living with them. At the same age as Margaretha, 40, Catharina also could be Sophia Dorothea's mother.
While both women could have been her mother, one hadn't had a child in 10 years, while the other had three children, the youngest of them 3 years old. While there are obviously "surprise" pregnancies, it seems much more likely that Johann Georg Meier and Margaretha, active in having children and raising a family, were Sophia Dorothea's parents.
I am not adding parents yet until further research can be done. I'd like to get my hands on a Dobrinka census and see if I can confirm her birth there.
Sophia Dorothea married Johann Martin Zulauf around 1793 and the couple went on to have at least five documented children:
Head of the Household Sophia Dorothea Zulauf, age 64
Child #1 Friedrich Zulauf, age 40
Wife of Child #1 Anna Dorothea Zulauf, age 39
Grandchild #1 Georg Heinrich Zulauf, age 18
Grandchild #2 Johann Kaspar Zulauf, age 16
Grandchild #3 Katharina Susanna Zulauf, age 14
Grandchild #4 Ernst Friedrich Zulauf, age 12
Grandchild #5 Katharina Margaretha Zulauf, age 10
Grandchild #6 Christina Margaretha Zulauf, age 7
Grandchild #7 Johann Adam Zulauf, age 4
Grandchild #8 Johann Jakob Zulauf, age 2 ears 6 months
Child #2 Johannes Zulauf, age 29
Wife of Child #2 Anna Dorothea Zulauf, age 25
Grandchild #9 Eva Katharina Zulauf, age 6 months
Child #3 Gotlieb Zulauf, age 23
Sophia Dorothea is not named in the 1857 Grimm census. She had either remarried and was living in another household, or she was deceased. Had she survived, she would have been 64 years old.
↑ 1.01.1 Pleve, Igor. Einwanderung in das Wolgagebiet 1764-1767, Band 1, Heerstellung: Mecke Druck and Verlag, 37115 Duderstandt; Published 1999; page 317, family #11, Juergen Meier, 54, Lutheran, farmer from Austria; page 325; family #47, Johann Georg Meier, 48, Lutheran, handworker from Mecklenburg, Rostock.
The 1775 and 1798 Census of the German Colony on the Volga, Lesnoy Karamysh, also known as Grimm; Published by the American Historical Society of Germans from Russia, Lincoln, NE, USA; Published 1995; family #37, Martin Zulauf family.
↑1834 Census of Grimm in the District of Saratov, Russia, dated 2 February 1835; Translated by Brent Mai, Concordia University, Portland, Oregon; Published by Dynasty Publishing, Beaverton, OR, USA; Published 2011;
page 12, family #38, Sophia Dorothea Zulauf family.