Nugent was a child actor, first appearing on screen at age six in It Had to Be You (1947), where she and her sister Carol portrayed the same character at different ages. A few bit parts in forgettable films were followed by her landing a regular role in television's first family sitcom, The Ruggles (1949–52). Her film career then took off with supporting parts in several mid-fifties dramas, including Magnificent Obsession (1954) and There's Always Tomorrow (1956). Two of her best-remembered roles was as Jet Maypen for the Walt Disney Presents: Annette serial on The Mickey Mouse Club and as little Ann Carlson, as the little blind girl who flew around the world with Superman, on the "Adventurers of Superman". As she reached adulthood, her parts were mainly guest appearances on television shows, including the ABC/Warner Brothers western series, Sugarfoot. She gave up acting after marrying in 1961, but did cameos for two independent film productions during the seventies.

Judy married actor Buck Taylor in 1961. They divorced in 1983. The Taylors had a daughter Tiffany and three sons, Adam Carlyle Taylor (1966–1994), Matthew Taylor (born 1970), and Cooper Taylor (born 1975). The three sons were involved with acting, directing, or stunt work for motion pictures and television. The Taylors moved to Montana during the latter 1970s. There Adam was killed in a road accident in Madison County three days before his 28th birthday. Adam was married to Actress Anne Lockhart, daughter of June Lockhart.