This is what I have, but it is not consistent with your info.
I have no Elizabeth Anna Merkel listed as the daughter of George Merkel and Anna Hill, but I have another Anna Elizabeth Merckel (b. 6/4/1768).She was one of the 11 children of George Merkel (b. 9or7/27/1729, d. 2/17/1779) and (Anna) Christina Hill (b. abt. 1730, d.11/16/1803) who were married on 12/18/1750.Anna Elizabeth Merckel married Capt John Dunkel (9/20/1766-9/27/1823).
The following is the family of Christina Hill, wife of George Merckel.You will note that Christina and George were cousins because Maria Appolonia and George were brother and sister, being children of Johann Christian Mercklen.
Jacob Hill, b. 1716, m. Maria Appolonia Mercklen, issue 5 children Daniel Hill, b. abt. 1718, m. Helena Mercklen. Johannes Hill, b. abt. 1720 Christina Hill, wife of George Merckel Elizabeth Hill, m. to a Houseknecht Anna Hill, m. to Godfried Kraemer
If this is your Anna Elizabeth, then she and Captain John Dunkel had 11 children that I have info on.
My records have the wife of George Merckel listed as both Anna Christina Hill and as Christina Hill, but mostly she is mentioned as "Christina".Maybe that is the source of our differences.In any case, there is not a Elizabeth Anna Merkel listed as the daughter of this George and Christina.I'll have to check to see if there is an Elizabeth Anna Merkel elsewhere in my info and will let you know.