She was born in Devonshire, Bermuda, on January 22, 1923. Her father, Lieutenant Colonel Thomas Melville Dill (also the name of her great-grandfather, a mariner), was a former Member of the Colonial Parliament (MCP) (representing the Parish of Devonshire in the Parliament of Bermuda), Attorney General of Bermuda, and former Commanding Officer of the Bermuda Militia Artillery. Her mother Ruth Rapalje (née Neilson) had roots in New Jersey. Douglas' brother Bayard was a prominent Lawyer and Politician. Her sister Ruth was married to John Seward Johnson I, heir to the Johnson & Johnson fortune. Douglas' father was from a prominent Bermudian family, present on the island since the early 17th century.