Dodson was born in 1828 near Malmesbury in Wiltshire, England.[1] His father, Joseph Dodson, was an officer in the British Army. His mother was Isabella Dodson (née Reid).[2]Joseph Dodson was an older brother.[3]
As a youth, he emigrated to Halifax in Nova Scotia, Canada, to join a brother. Together, they went to Victoria, Australia and joined the Victorian gold rush. After that, he came to Nelson, New Zealand and joined his brother Joseph Dodson in his brewery business.[1] He married Emma Snow (born 6 January 1830) on 10 December 1857 at Nelson.[4] He came to Blenheim in the late 1850s and set up a brewery in that town.[1]
Dodson was a member of the Marlborough Provincial Council for three different electorates from 1860–1863, 1866–1870, and 1874–1875.[2] In the provincial council, he was the head of the Blenheim party for many years, and they quarrelled against the Picton party.[2] He was Mayor of Blenheim for four one-year terms (1870–1871 and 1883–1884). He represented the Wairau electorate from 1881 to 1890, when he retired.[5] In 1881, he beat the incumbent, Arthur Seymour.[6] He was challenged by Joseph Ward in 1884.[7] In the 1887 election, he was challenged by a former Mayor of Blenheim, George Henderson, and Sutherland John Macalister.[8][9]
His wife died in June 1883.[10] He died on 8 May 1892 at his home in Blenheim, New Zealand after a sudden illness and was survived by seven children.[1] He was buried at the Omaka Cemetery in his brother George's family plot in the Old Cemetery section.[11][12]