Joel - Eve. She converted Adam to God's plan when she gave him the fruit.
Women started serving as missionaries from the very beginning of church history, as they often served with their husbands on missions.
In 1830 Lucy Mack Smith accompanied Hyrum and preaches to her family on a trip to Pontiac Michigan. In 1850 Louisa Barns Pratt is "blessed, set apart, and ordained" by Brigham Young to serve with her husband Addison in the Society Islands.
In 1865 thirteen women were called and set apart to serve with their husbands and for the first time appear on official church records as missionaries.
Caroline Barnes Crosby who traveled with her family to Utah in 1848, began writing her memoirs early in the 1850s while she and her husband were working as Latter-day Saint missionaries in the Society Islands (Tahiti).
Julina Smith left Salt Lake City in 1885 to accompany her husband, Joseph F. Smith, on a mission to the Sandwich Islands (Hawaii). She was commissioned by the Church to serve as a midwife and helped deliver many Hawaiian babies.

Later on President George Q. Cannon and Apostle John W. Taylor prepared the church for single women missionaries in the April 1898 general conference. After citing numerous requests for women to serve missions, President Cannon explained:

"We do not want unwise women sent any more than unwise men, because they could do more injury than they could do good. But if they can get a recommend from their Bishops as wise, suitable women, we will set them apart. . . .It seems as though the Lord is preparing the way for the women of this Church to do some good in this direction. To some lands and under some circumstances suitable women might go. . ."
(President George Q. Cannon, Conference Report, (April 1898): 7.)

In 1898 Jennie Brimhall and Inez Knight receive calls to England as the first single full-time proselyting sister missionaries. Jennie Brimhall served from April to November and was issued an honorable release due to health concerns. Liza Chipman replaced her, and she and Inez Knight continued to serve until their release in May 1900.

Some references:
"Not Invited, But Welcome: The History and Impact of Church Policy on Sister Missionaries", Tania Rands Lyon and Mary Ann Shumway McFarland

Calvin S. Kunz, "A History of Female Missionary Activity in the Church of Jesus Christ of Latter Day Saints, 1830-1898" (M.A. thesis, Brigham Young University, 1976): 35-36.