Evidence from emigration, church ordinance, and church records (Perpetual Emigrating Fund) proves that the Wayman family traveled to Utah sometime between 1868 and 1870. They sailed to America in 1868 on the John Bright. But the first documentation to place them in Utah is a church ordinance performed for Elizabeth in September 1870. Further research is needed to confirm the year they came to Utah and the name of the company they traveled with.
Her given name is "Mary" on the ship manifest and Mary Elizabeth Wayman McKay on Find A Grave website.