M (1978, 33)
FMMMMM (1839, 49) Lois Knapp
FMMMM (1839, 27) Louisa Walker
FMMMF (1831, 24) Edson Barney
FMMFM (1840,33) Joanna Case Worden
FMMFF (1852, 47) Elisha Barrus Keyes
FMFMMM (1848,59) Delia Deliverance Byam
FMFMMF (before 1836, before 49) Tillison Reed
FMFMM (unknown) Sally Ann Reed
FMFMFM (before 1838, before 54) Millicent Waite
FMFMFF (before 1846, before 62) Naham Curtis
FMFMF (1833,15) Joseph Curtis
FMFFMM (1833, 41) Experience Wheeler
FMFFMFM (before 1847, before 78) Amy Ward
FMFFMF (before 1833, before 33) Joseph Hancock
FMFFM (1847,12) Amy Experience Hancock
FMFFFM (1831,36) Alta Adams
FMFFFFM (before 1847, before 78) Amy Ward
FMFFFF (1830,37) Solomon Hancock
FMFFF (1834,8) George Washington Hancock
FFMMM (before 1862, before 55) Anna Wylimann
FFMMF (1861,58) Casper Wintsch
FFMM (1861,10) Anna Caroline Wintsch
FFMFM (1862,70) Elisabeth Luethi
FFMF (1861,30) Nicholas Muhlestein
FFFMMM (1843,37) Hannah Whitcomb
FFFMMF (1843,37) Gilberth Haws
FFFMM (1843,15) Lucinda Haws
FFFMF (1843,21) Shadrach Holdaway
FFFM (1864,8) Mary Elizabeth Holdaway
FFFFM (1841,39) Sarah Adams Bitely
FFFF (1866,35) Charles Conrad
There it is, to the best of my ability, using the New Family Search website, and taking into account not a few peculiarities.
Each line shows the relationship to Elizabeth, the year of the ancestor's baptism and their age at baptism, and finally the ancestor name (maiden names are used for all women).
Some dates (and therefore ages) are best guesses. The notation "before" gives the date/age of the ancestor's death, when it is strongly believed that they were baptized during their lifetime. Often, this is believed because their death occurred at a place and time where/when the Mormons were gathered, such as Winter Quarters or Clay County, Missouri.
In the case of Anna Wylimann, we know from her daughter's account that she was baptized about a year before her daughter. We also know that she died while crossing the plains on 4 September 1862, and was buried on the prairie.
In the case of Experience Wheeler and her second husband**, Joseph Hancock, I am relying on the accuracy of the linked account. Interestingly, these two appear to have been first cousins. Joseph and Solomon Hancock were brothers, making their children Amy Experience and George Washington first cousins.
The short answer to her question is that Elizabeth has both a parent who is a recent convert, and the first in a family, as well as a parent who is a product of a complete ancestry of people who joined the Church within the first few decades of its organization. I have attempted to identify the first in each family line to convert, but have also included a couple of cases of an ancestor baptized at age 8. To my knowledge, all of the ancestors missing from this list, but closer to Elizabeth, of course, were baptized at 8.
It was difficult to put all this together, partly because the work has been done for the dead sometimes many times over, and people who we are sure were baptized during their lifetimes often show a baptism date/temple well after their death. In some cases, the website showed a confirmation date during the lifetime, and in those cases, I used the same year for the baptism date. In the case of Sally Ann Reed, all of the LDS ordinance dates are hidden because someone has decided to do all of her work yet again. However, I am very sure that she was baptized, at least, during her lifetime.
*By "the Church" is meant "The Church of Jesus Christ of Latter-day Saints." (see style guide)
**Edited the next morning. Here is a screen scraping of a pedigree section that led me to look deeper into the situation:
The question raised in my mind (and resolved by reading the story of her mother's life) was how Amy could have the family name Hancock if her father was a Rudd. He wasn't. The pedigree section on the website was based on an incorrect resolution of conflicting data.