Patriarchal Blessing March 21, 1843, in Nauvoo, Hancock, Illinois, United States. officiated by Hyrum Smith
Endowment January 21, 1846, at the Temple in Nauvoo, Hancock, Illinois, United States
Sealed to Spouse in 1842 and January 26, 1846
Biographical Notes (published on Find A Grave Memorial, unsourced):
She was baptized a member of The Church of Jesus Christ of Latter-Day Saints on July 29, 1839 by Elder John P. Greene. She was living with her brother, David, at Haun's Mill at the time when the massacre of the saints occurred there. She and other members of her family were under the necessity of secreting themselves to the woods to escape the mob. Desdemona arrived in Salt Lake City in October of 1848 in the Willard Richards Company, and lived there for nearly forty years, residing at 375 West 400 South in the Downtown district of Salt Lake City. She was a quiet, unassuming, faithful woman and was greatly respected by all who had the pleasure of her acquaintance. Desdemona worked as a tailoress for most of her life, and completed her autobiography a few years before her death.
Desdemona married Joseph Smith Jr. in 1842 in Nauvoo, Illinois. They were later sealed on January 26, 1846 in the Nauvoo LDS Temple. After his death, she later married Ezra Taft Benson on January 26, 1846 in the Nauvoo LDS Temple.
She passed away in 1886 in the Utah Territory, United States. 
Source: S1 1880 United States Federal Census, Salt Lake City, Salt Lake, Utah; Roll: 1337; Page: 47B; Enumeration District: 043.
Source: S5 Salt Lake County, Utah, Death Records, 1908-1949, Ancestry.com. Original data: Utah, Salt Lake County Death Records, 1908-1949. Salt Lake City, Utah: FamilySearch, 2013.
Source: S8 Membership of The Church of Jesus Christ of Latter-day Saints, 1830-1848, Ancestry.com. Original data: Black, Susan Easton, compiler. Membership of The Church of Jesus Christ of Latter-day Saints, 1830–1848.50 vols. Provo, Utah: Brigham Young University Religious Studies Center, 1989. Private Donor.
It may be possible to confirm family relationships with Desdemona by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share DNA with Desdemona: