The Cook family came to Utah in either 1851 or 1852. They likely came in 1851. But the first documentation to place them in Utah is a child born in 1852. Further research is needed to narrow the year of their travel.
Her name is "Ealand Cooke" on the 1850 Iowa census and "Ellen" on the 1860 Utah census. Her surname is"Smith" on Find a Grave website.