In late 1960, they had an Australian hit with "My Secret" which got to #28 nationally. After a couple more lesser remembered songs they went off to tour the Far East. While performing at an hotel in Hong Kong in the spring of 1964 Judy Garland saw them and was impressed. (Click to see photo with Peter, Judy and Chris). She got them bookings and brought them to London, where they were her opening act. She also introduced Peter Allen to her daughter, Liza Minnelli, and the two became engaged. The Allen Brothers made their American debut at the Diplomat Hotel in Miami in December 1964, then, they moved to New York. For the rest of the 1960s, they appeared in clubs around the U.S., notably at the various Playboy Clubs. After a lengthy engagement, Allen and Minnelli married on March 3, 1967.
The rest of Peter Allen's story is well documented and easy to locate on the internet. Here is their very first hit "My Secret" in glorious mono :