Allan had previously toured the Caribbean with Australia in 1965 but did not play a Test due to illness.
Remarkably, Allan also took 10 wickets in an innings in a Brisbane club game in March of 1966.
Allan's first-class career spanned a decade from 1959 to 1969. He took 206 wickets at 26.10, including 12 five-wicket hauls and three 10-wicket hauls in 57 matches.
His post-cricket career featured a variety of roles including with the Brisbane City Council, as a hotel publican and civil celebrant on Hamilton Island.
Queensland Cricket Chairman Chris Simpson honoured Allan upon his passing.
"Peter had great skill as a bowler which was also mixed with determination," Simpson said. "He typified that strike bowler role in the teams he played for. He served on the executive committee of the Queensland Cricket Association from 1985 to 1991 and was generous with his time and insights for any aspiring player who sought him out.
"His feat of taking 10 wickets in an innings remains a high point in Australian cricket. Peter made a wonderful contribution to cricket in Queensland and on behalf of Queensland Cricket, we thank him for his service to the game."