Soon after graduating from Ireland's Albert Agricultural College, Glasnevin, Alexander Crawford migrated to Australia for health reasons. It is though he spent some time in Queensland, then surveying routes through Western Australia for the transcontinental railway and finally managing a butter factory in Ballan, Victoria. In 1881 took over the part-ownership of a sheep run in Moorarrie, Western Australia, but left for Perth the following year.

Crawford then travelled to Europe to observe dairy farming practices and upon his return was appointed manger of a travelling Victorian dairy. This job entailed travelling by rail to thirty-eight centres providing practical demonstrations and lectures on cheese and butter production and hygienic operation of equipment. He also wrote several reports and articles on a wide range of subjects within the field of dairy farming and production.

In 1891 he took over the management of the Victorian Creamery and Butter Company which folded in 1895 after Crawford had left. A Royal Commission found irregularities in the accounts of the company, and although no official blame or charges were laid against Crawford his reputation was said to be irreversibly damaged. From 1896 to around 1920 Alexander Crawford worked for the Western Australian Bureau of Agriculture. As part of this position he was appointed chief-inspector under the Rabbit and Vermin Acts and travelled across the outback checking the rabbit proof fences. He was also an active member of the Wesley Church in William Street Perth and is commemorated there by a plaque.