Eliza sailed to America in 1862 on the ship William Tapscott.
Her name appears on both the 1862 Ansil P. Harmon and 1862 Horton D. Haight rosters. It is possible she traveled in either or even in both. Further research is needed.
Birth and death dates are confirmed by the death certificate. Her surname is "Law" on the 1870 Utah census, death certificate and Find A Grave website