Alex Birnie was born in Melbourne on 7 April 1889. His father, Norman, was an engineer in the Victorian Railways. Norman married Barbara Irving, whose family were farmers in Gippsland. Alex was educated at Melbourne Grammar School and Geelong College, and entered the University of Melbourne in 1910 to study medicine, graduating in 1914. Alex offered for service in the Australian Army Medical Corps but was told that they had all the doctors they required; so he sailed for England and enlisted in the Royal Army Medical Corps, serving in France and Belgium and experiencing the horrors of trench warfare. He was twice wounded and was awarded the Military Cross. The citation read:

'In going forward with the stretcher bearers to form an advanced aid post, he was wounded in the shoulder by a piece of shell, one of the stretcher bearers being killed at the same time. He continued dressing the wounded in a most advanced line and even penetrated the enemy line of posts in search of casualties: keeping at his work until relieved some eight hours later.'

He rarely spoke of his war experiences, but was always eager to help the returned men at the Repatriation Hospital for many years. While on leave in England he married Dorothy Elizabeth Campbell, a nurse at St Bartholomew's Hospital. She remained his devoted companion until her death in 1976. They had one son, Norman, who graduated in medicine and is now a much respected general practitioner in Glen Iris. When he returned to Melbourne in 1918 the city was in the grip of an influenza epidemic. The large Exhibition Building was converted into a temporary hospital and Alex was involved in caring for the many patients. He took his MD at Melbourne in 1920.

On his return to civilian life Alex was appointed clinical assistant at the Alfred Hospital and in 1924 was appointed honorary physician to outpatients. He became honorary physician to inpatients in 1936 and remained in that role until his retirement from the staff in 1949. He was very conscientious in caring for his patients and in his teaching of his students. He was always encouraging and helpful to his younger colleagues, and although strict in his standards was loved by all.