It depends on the term (Prime Minister.)

If you count Premiers as heads of Westminster Governments. Than Thomas Playford IV of South Australia would be the longest serving from 5 November 1938 – 10 March 1965. He lead a State Government which loosely fits the term.

If you consider just the term Prime Minister. That that would be Sir Godfrey Huggins of Southern Rhodesia, than the Central African Federation, than Rhodesia from 12 September 1933 - 2 November 1956