Dundas was born in Edinburgh to Elizabeth and James Dundas. He schooled at Westminster
                     and Oxford, where he received his BA in 
1820, and his MA two years later. Dundas's life was a blend of law and politics, and by
                     
1840, he was appointed to the Queen's Council. On 
10 July 1846, he became solicitor-general under 
Lord John Russell. Dundas was knighted on 4 February, 
1847, but would resign from office due to inconstant health in 
March of 1848. A more comfortable post was offered, as principal clerk of the House of Lords, but
                     Dundas declined the position. He took office again in 
May of 1849 as judge-advocate-general; thereafter, he was sworn into the privy council on June
                     29th of the same year. He retired from political life altogether in 
1852.
In his role as Solicitor General, Dundas, along with Attorney General 
John Jervis, was instrumental in the Crown's deliberations on the 
Hudson's Bay Company's land-grant status following the 
Oregon Treaty of 
1846. The two men signed-off on a 
Case,
 attached to an 
1847 despatch, that detailed the complex legal arguments surrounding the 
HBC's position.