Here is the family legend regarding this baby's birth and death. (The place where it happened is not entirely correct - see below.) From the book "Carter Pioneers of Provo Utah," we read of Sophronia Babcock Carter's agony as she delivered this baby. Neither survived the ordeal and mother and child "were buried in an unmarked grave on the lonely Iowa prairie beside the Carter wagon wheel tracks which countless wagons were soon to follow."

The account in the Carter book is not entirely correct. Domninicus Carter was living in Carterville at the time of the baby's birth and death. Here is a first-hand account of Sophronia's burial:
In a journal entry from Nancy Naomi Alexander Tracy found in "Life History of Nancy Naomi Alexander Tracy Written by Herself" she states that Dominicus Carter's brother William's wife Hannah Cordelia was buried at the Carterville Cemetery and that Dominicus' wife (and surely the baby) were buried there too by the side of Nancy's baby boy.

Carterville was one of the "Winter Quarter" settlements near what is now Council Bluffs, and upwards of 200 Mormon pioneers were buried in its cemetery. After the exodus of the pioneers to Utah, the cemetery fell into disrepair and was eventually forgotten. It has now been located - in a farmer's field. See the newspaper article about Carterville cemetery, in the Salt Lake Tribune, 18 October 1902, page 9.
http://udn.lib.utah.edu/cdm/ref/collection/sltrib22/id/147503

GENDER: The family records of some Carter descendants have the gender of this child as male. Others have the gender as female. The fact is that Dominicus did not state the gender of this child in his record (he simply wrote the word "Baby"). Nor is there any other historical record about the birth. The early histories about the event simply refer to "the child," and later attempts to assign either male or female gender can only be considered guesses.