Dowd studied law at the University of North Carolina at Chapel Hill and received his degree in 1856. 1857 and 1858 he worked as a teacher. In 1859 he was admitted to the legal profession and practiced in Charlotte. During the Civil War he served in the Confederate Army. After the war he was again engaged in his former occupation. From 1869 to 1871 Dowd held the office of mayor of Charlotte. After that, he was from 1871 to 1874 president of the Merchants & Farmers' National Bank, and from 1874 to 1880 president of the Commercial National Bank of Charlotte.
Dowd was elected as a Democrat to Congress and represented there on 4 March 1881 to 3 March 1885 the state of North Carolina in the U.S. House of Representatives. In the elections of 1884, he did not run. He died in 1898 in Charlotte, and was buried in the Elmwood Cemetery.