I really don't know anything about the history of this doll, I wish I did. My mother was always going to catalogue her doll collection and never did!.
Her name is written by hand into the bisque on the back, it is difficult to see and I missed it for quite a while -- it's large enough, but the top of her dress is sewn -- just tacked in a couple of places -- onto the cloth body just below the bisque shoulders and it's hard to pull back to get a clear view of the writing, but the writing itself is quite clear.
Interestingly, there was a show on the history channel the other night about the White House celebrating its 200th birthday, and there was a segment about John and Abigail Adams -- they showed her portrait and the dolls face is really a good representation, assuming the portrait was!
My mother's name was Frances Carleton Sawyer, she lived most of her life in Massachusetts, a few years in DC, collected dolls from early adulthood, though did not have a huge collection, she was a member of the local and national doll clubs, died in 1988 at the age of 85. I I wish I could tell you when, where, how and why she got this doll -- she had no other first ladies dolls and I don't think it was a particular interest of hers so perhaps this was a gift.