Bobby & Laurie their peak in late 1964, busily touring the country and appearing in numerous concert and television performances. They had dozens of engagements and personal appearances every week, with as many as six shows on a Saturday night. One unusual performance was playing 'Tweedledum' and 'Tweedledee' in a Christmas pantomime production of "Alice in Wonderland" at the Tivoli Theatre in Melbourne in December 1964. In early 1965 the pair appeared on the "Teen Scene" music television show on the ABC, where they were famously dragged off the stage by screaming female fans. They appeared in the premiere episode of Channel 0's
Tweedledum and Tweedledee the most celebrated and most frequently quoted (and sometimes misquoted) epigrams", satirising the disagreements between George Frideric Handel and Giovanni Bononcini, written by John Byrom (1692–1763): Although Byrom is clearly the author of the epigram, the last two lines have also been attributed to Jonathan Swift and Alexander Pope. While the familiar form of the rhyme was not printed until around 1805, when it appeared in "Original Ditties for the Nursery", it is possible that Byrom was drawing on an existing rhyme. The characters are perhaps best known from Lewis Carroll's "Through the Looking-Glass and what Alice Found There" (1871).