Plumer was born in Epping, New Hampshire on February 7, 1789, a son of Sarah "Sally" (Fowler) Plumer and William Plumer. He attended Phillips Exeter Academy and graduated from Harvard College in 1809. Plumer then studied law with his father, attained admission to the bar in 1812, and commenced practice in Epping.

In 1816, Plumer was appointed a United States loan commissioner for New Hampshire, and he served until 1817. He was a member of the New Hampshire House of Representatives in 1818.

In 1818, Plumer was elected as a Democratic-Republican to the Sixteenth Congress. He was reelected to the Seventeenth Congress in 1820, and as a Adams-Clay Republican he won reelection to the Eighteenth Congress in 1822. He served from March 4, 1819 to March 3, 1825 and was acting chairman of the Judiciary Committee in the Seventeenth Congress, following the January 1823 resignation of Representative Hugh Nelson, who had been appointed U.S. Minister to Spain.

After leaving Congress, Plumer resumed practicing law. He was a member of the New Hampshire Senate from 1827 to 1828. He served as delegate to the New Hampshire state constitutional convention in 1850. Plumer authored several works in his later years, including a biography of his father that was published in 1857 and a book of religious-themed poetry, 1846's Lyrica Sacra.

Plumer died in Epping on September 18, 1854. He was interred in the burial ground on the family estate near Epping.

In 1820, Plumer married Margaret Mead Frost. They were the parents of three children—Mary Elizabeth (b. 1822), William (1823-1896), and Sarah Adeline (1826-1828).

• United States Congress. "William Plumer Jr. (id: P000394)". Biographical Directory of the United States Congress.
• William Plumer Jr. at The Political Graveyard
• Magazine article: William Plumer Jr. The Granite State Monthly. March–April 1889. Page 76.