Haddon's Quaker father, John Haddon, bought a 500-acre (2 km²) tract of land in Gloucester County in the English colony of West Jersey to escape religious persecution. However, poor health kept him from settling there. Haddon, a single woman, set sail from Southwark to the New World in 1701 without her family. Shortly after her arrival, she made a marriage proposal to John Estaugh (1676–1742), a Quaker minister, and they were married in 1702. Their courtship was described by Henry Wadsworth Longfellow in "Elizabeth", a poem from his Tales of a Wayside Inn.
Haddon and John had no children, but they brought her sister's son, Ebenezer Hopkins, to America from Southwark when he was about five, and raised him as their son and heir. Ebenezer was the son of Benjamin and Sarah (Haddon) Hopkins, and the grandson of William and Katheryn Hopkins. Ebenezer was the founder of the Hopkins family of Haddonfield, New Jersey.