Their child died soon after. By October of 1710 they were settled in Elizabethtown, which is no longer on the map. It was part of the West Camp settlement of Palatines indentured to make tar for Britain's navy. Their second known child, Anna Margaretha, was born 15 Apr 1712 in Elizabethtown. She was the only one of the Wagner children to be born in the camps.
Good research makes for sound genealogy.
So far, the births, marriages, and emigration of the Wagners are supported by church records and the Hunter subsistence lists, all part of a written record of their lives. His marriage and his son's baptism are likewise recorded on the church books. Subsistence records prove the existence of a surviving child in July 1710, and fail to find him thereafter, hence we assume his death. The government was careful about those records because they expected repayment per head for all expenses Peter and his family incurred. Their residence in Elizabethtown is supported by the same subsistence and other records.