 Dobson was full brother to Henry Dobson and half-brother to William Lambert Dobson, and Frank Dobson.Alfred Dobson was educated at The Hutchins School, Sandy Bay, Hobart and became a student of the Inner Temple on 20 April 1872, being called to the English bar on 26 January 1875.Returning to Tasmania, Dobson was called to the bar there on 10 September 1875, and was a member of the Tasmanian Legislative Assembly from 14 June 1877 to May 1887.