I found his photo on Trove, and the Australian War Memorial provided these details:
"First World War Embarkation Roll - Alan Bellingham Cairnes. Service number: 2622. Rank: Private. Roll title: 58 Infantry Battalion - 6 to 9 Reinforcements (October 1916 - August 1917) Date of embarkation: 2 October 1916. Place of embarkation: Melbourne."
There is also information that at that time he was single and a bookkeeper living at 83 The Avenue, in the suburb of Coburg, and that his father, William Bellingham Cairnes, lived at 7 Bancroft St, Bendigo. He served in 58 Battalion and was wounded in action in France on 26/9/1917. He survived the war, and in 1923 he was at Vergemont Station near Longreach, Queensland.
Alan Bellingham Cairnes, 1916