Hi Mary, Elizabeth White was born abt. 1706, but I do not have dates for her death. The Carrier family German link theory is not one I have heard before! How do you know the family were members of the Church of the Brethren? I would love to chase this down.
W. John Carrier, Sr. certainly spoke English (although this is not to say he did not speak German as well). Of course, the best way to find out is for a known male descendant of W. John Carrier to match his DNA with that of male French and/or German Carriers today and see where the genes fall! DNA is a great tool for determining possible countries of origin for families.
Here is what I know about the Carrier surname. It shows up in France often and there are many French Canadians with the surname Carrier that do not seem to be linked with the W. John Carrier line. I was lucky enough to have a contact in France doing some research for me several years ago, and it turns out that the surname Carrier in France meant "quarry worker." More specifically, someone who "carried" the stone from the quarry. So, in France at least, Carrier was a trade name.
Carriers also show up in the Northeast of the U.S. as well as in Louisiana, all areas with historic French Influence.
The W. John Carrier line, however, shows up in written records in Somerset England in the late 1600s, with immigration not occuring until the 1750s, So at least one generation of Carriers lived their entire lives in England.
If the W. John Carrier branch had been in England long term, it is entirely possible the surname was originally French and came to England afer the Norman conquest of 1066. It is also possible that Carrier was an original English trade name as well. Of course, this is lots of conjecture, but it is good fun!