Dorman was born in Dublin, and was brought up as a Quaker. He served with the Royal Navy and with the Young Men's Christian Association, later working in insurance. Around 1885, he was living in Derry and was already regarded as one of the most prominent socialists in the city. Dorman later moved back to Dublin and joined the Independent Labour Party. There, he co-signed the letter which invited James Connolly to become the organiser of the Dublin Socialist Society.
Dorman seconded the proposal to re-form the Dublin Socialist Club as the Irish Socialist Republican Party (IRSP), and spoke alongside Connolly at the party's official launch, on the Dublin Custom House steps. He moved to Limerick later in the year, but was unable to establish a branch of the party there, and resigned from the IRSP in June 1897.
Dorman remained a Christian socialist, and continued to give public speeches when he moved to Belfast in 1912. When the Belfast Labour Party was established, he became active in it and when, in 1924, it was reconstituted as the Northern Ireland Labour Party (NILP), he was elected as its first vice-president. Later in the year, he stood to succeed Joseph Davison as alderman for the Court ward on the Belfast Corporation, but he was defeated by independent Unionist John William Nixon. The Manchester Guardian reported that several women supporting Nixon were arrested on the day of the election, on charges of personation.
In 1925, Dorman was elected as the first NILP member of the Senate of Northern Ireland. He served until 1933, when he lost his seat due to the reduced number of NILP members in the Commons. He stood again in 1935, following the death of George Clark, but was defeated by the Ulster Unionist Party candidate William Gibson by 35 votes to 5.
Dorman was regarded as an expert on Irish literature of the nineteenth century, and was also known as an advocate of temperance. During the 1930s, he campaigned for the reunification of Ireland, and supported Nationalist Party candidates in several elections. Dorman visited Liverpool in mid-1937 to attend the funeral of his brother, but he died suddenly, while addressing a religious meeting, and was buried alongside him.
- "Northern politician's tragic death", Irish News, 25 August 1937
- Fintan Lane, The origins of modern Irish socialism, 1881-1896, p.112
- Fintan Lane, The origins of modern Irish socialism, 1881-1896, p.215
- Donal Nevin, James Connolly: A Full Life, p.60
- Fintan Lane, The origins of modern Irish socialism, 1881-1896, p.218
- Fintan Lane, The origins of modern Irish socialism, 1881-1896, p.221
- Fintan Lane, The origins of modern Irish socialism, 1881-1896, p.190
- Joe Keenan, The Labour Opposition of Northern Ireland, p.17
- "Ulster's last ditch a court of law", Manchester Guardian, 15 August 1924
- "Women change clothes and go on voting", Manchester Guardian, 28 August 1924
- The Northern Ireland Senate, 1921-72, Northern Ireland Elections]
- D. R. O'Connor Lysaght, "Between comrades: James Connolly, letters and correspondence, 1889–1916", History Ireland, vol.16 no.3
- "New Ulster Senator", Daily Mirror, 1 May 1935, p.7
- Untitled article, Manchester Guardian, 25 August 1937, p.5