Penelope Johnston was born in North Carolina in about 1741. Penelope grew up with immense privilege as her father Gabriel Johnston served as North Carolina's colonial governor from 1734 to 1752 and her mother was the stepdaughter to another former governor, Charles Eden, and the heiress to a large fortune. Despite this privilege, Penelope's early life was also beset with loss. Penelope's mother died shortly after her birth and her father died when she was eleven, leaving her an orphan with a considerable fortune. Robert Dinwiddie, Virginia's governor, assumed guardianship of Penelope and raised her alongside his own children with a variety of tutors.

In 1758 she eloped with John Dawson, a fellow orphan from a prominent Virginian family who had experience as a lawyer and surveyor. The Dawsons settled in Bertie County at Eden House, a plantation Penelope's family had held for generations. Although her father had been a crown officer, Penelope allied herself with the Patriot cause. In 1774 she and several of her Johnston cousins, as well as many other local women signed a nonimportation agreement that later became known as the Edenton Tea Party Resolves. She later died in Bertie County in July 1797.