Born in Tenafly, New Jersey, Hamer was the youngest of three sons of Arthur Walter John, Sr., a men's shirt salesman and Dorothy Hamer (née Chretin), a former silent film Actress. He had two elder brothers, John and Walter. As a child, Hamer was nicknamed "Rusty" because of his red hair and freckles. Due to his parents' involvement in community theatre productions, Hamer and his brothers also began performing in stage productions. As a toddler, Hamer memorized and recited stories and performed skits for Service club luncheons, women's clubs and church groups. In 1951, the Hamers moved to Los Angeles where Arthur Hamer worked as representative for a manufacturer of men's sport shirts (Arthur Hamer died eight months after his son was cast in The Danny Thomas Show). Shortly after arriving, Hamer's elder brother John was discovered by an agent while performing in a local stage production in which Hamer was also performing. The agent signed both boys to a film contract. The following year, Hamer won his first acting role in the 3-D Western Fort Ti, starring George Montgomery and Joan Vohs.

In 1953, entertainer Danny Thomas' secretary saw Hamer in a stage production and was impressed by the child's talent and charm. She suggested that Thomas audition Hamer for a role in his upcoming sitcom Make Room for Daddy. Thomas was also impressed by the 6-year old and cast Hamer as his precocious and quick-witted son, Rusty Williams. Thomas later said of Hamer, "He was the best boy actor I ever saw in my life. He had a great memory...great timing and you could change a line on him at the last minute and he came right back with it." Make Room for Daddy debuted on ABC on September 29, 1953 and, while critically acclaimed, garnered poor ratings. After three seasons, the series moved to CBS where it was re-tooled and retitled The Danny Thomas Show. The retooled version quickly became a hit with audiences and was a Top 20 hit for its remaining seven seasons. During the run of The Danny Thomas Show, Hamer attempted to launch a singing career. He first performed a song in a 1956 episode of Danny Thomas entitled "The Talented Kid". In 1959, Hamer released his only single, a "rockaballad" called "Two-of-a-Kind" (with the b side "If Only Mother Would Let Me") written by Wally Gold and Aaron Schroeder, through Mercury Records. The single was a commercial failure and Hamer never released another single.

On February 8, 1960, Hamer was awarded a star on the Hollywood Walk of Fame for his work in television. His star is located at 6323 Hollywood Boulevard.

By late 1963, The Danny Thomas Show had garnered five Primetime Emmy Awards (among other awards) and was still ranked in the Top 10. However, Danny Thomas announced that he had decided to end the show in order to produce and star in other projects. After the series ended, 17-year old Hamer enrolled at Palisades High School (years later restructured as Palisades Charter High School), but had difficulty adjusting to public school as he was accustomed to being privately tutored on the set. Shortly before graduating in June 1964, Hamer granted an interview with reporter Bob Thomas. He stated that he intended to continue his acting career and hoped to branch out into dramatic roles. Hamer said that he was under consideration for roles in several television series including Mr. Novak, Arrest and Trial and Ben Casey. Hamer also said that he planned to attend college on the advice of Danny Thomas, whom he considered a second father, since his own father had died in 1953.

A year after The Danny Thomas Show ended, Hamer reprised the role of Rusty Williams in the reunion special The Danny Thomas TV Family Reunion, which aired on NBC. On December 27, 1966, Hamer underwent emergency surgery at Santa Monica Emergency Hospital after sustaining a gunshot wound to the abdomen when a gun he was carrying in a shoulder holster slid out, fell to the ground and discharged. Hamer was carrying the gun after having just returned from an overnight hunting trip. After recovering, he appeared in a second reunion special, "Make More Room For Daddy", that aired during a segment of the NBC anthology series The Danny Thomas Hour, in 1967. Throughout the mid to late 1960s, Hamer continued to attempt a transition into adult roles and, according to Danny Thomas, enrolled in acting classes, but was unable to land any acting jobs. By the end of the decade, he had grown increasingly bitter and depressed over his waning career. To support himself, he began working for a messenger Service in Los Angeles and later worked as a carpenter's apprentice. Hamer's only post Danny Thomas Show acting role was a guest spot on the CBS sitcom Green Acres, that aired in November 1969.

In the 1970s, Hamer moved to southwestern Louisiana where he worked on an off-shore oil rig for Exxon and delivered newspapers. In 1976, he relocated to DeRidder, Louisiana to be closer to his ailing mother, Dorothy, who was suffering from Alzheimer's disease and lived with his elder brother John. John Hamer had moved to the area and opened a cafe where, in his final years, Hamer occasionally worked as a short order cook.

In October 1981, Hamer reunited with former co-stars Danny Thomas and Angela Cartwright. The reunion was televised as part of the ABC special What Became Of...?, that aired on October 25.

On the night of January 18, 1990, John Hamer found his brother's body in his trailer home in DeRidder, Louisiana. Hamer had shot himself in the head with a .357 Magnum revolver.