[1] Dobson's political career began on 12 August 1891, when he was elected to the Tasmanian House of Assembly representing the electorate of Brighton.

He was quickly made Leader of the Opposition the next month, and became Premier of Tasmania on 17 August 1892 after the fall of Philip Fysh's government.

He also promoted Tasmania as a tourist destination and fruit-growing centre, attributes which it remains known for today.

Economic factors required him to make difficult decisions, and when a proposed retrenchment program was rejected in the Parliament, Dobson obtained a dissolution from the Governor, and then resigned as Premier on 14 April 1894 when the situation remained unchanged after the election.

[5][6] After retiring from politics, Dobson turned his efforts to promoting Tasmanian tourism.