According to Official Guinness Records,
The first woman to fly faster than Mach 1 was a famous, female aviator named Jacqueline Cochran (USA). Better known as Jackie, Cochran was born in 1906 and became one of the pioneering women of aeronautics. She was a friend of Chuck Yeager, the first person to break the sound barrier. He helped her to make the transition to jet-powered aircraft, and she then soon achieved a number of new aviation records. On 18 May 1953, she flew an F-86 Sabre past Mach 1 becoming the first woman to break the sound barrier. She went on to set a world speed record of 1,429 mph (2,300 km/h) in 1964 and no fewer than eight speed records in 1967, when she was over 60 years old!
For a complete list of 1953 records, please visit 1953 Guinness Records in United States.