Alice was a great granddaughter of Jeremiah Phillips, a Revolutionary War Veteran who was born in England in 1745 and died in Kentucky in 1805. Alice died in Clay Township per her death certificate.

Missouri Death Certificate 1804 shows the following:
Occupation - Farmers wife
Father - Thomas Jennings, birthplace Kentucky
Mother - Lucy Phillips, birthplace Kentucky
Informant - Mrs. H. Long, Wheeling, MO
The death certificate shows her name to be Thomas Alice Bailey.

Following is some information from Kathryn (Findagrave Mbr 50471305)
It is an odd thing to for Alice's legal first name to be Thomas! She is the youngest sister of my ggg-grandmother Elizabeth Evaline Jennings, of whom is written about in extensive family history written by my g-grandmother. I have recently researched her more as I found a photo of her and her family. She is commonly called "Alice" by family, and most other family members are called a by a shortened nickname for their first or middle name as well in that era of family history as compared to legal documents. For "Alice" Thomas Alison I have the following documents in my Ancestry profile:

1850 Census: Thomas Alison Jennings, F, age 5, with her widowed mother Lucinda Tate Jennings
1860 Census: Thomas A. Jennings, F (female)
1863 Marriage Record: Thomas A. Jennings (wife) marries Simpson N. Bailey
1870 Census: Alice Bailey
1880 Census: Alice T. Bailey
1890 Census: Thomas A. Bailey, F
1900 Census: Thomas A. Bailey, F
1910 Census: Thomas A. Bailey, F
1920 Censsu: Thomas A. Bailey, F
She is identified in other Ancestry family trees as Thomas Alice/Alison Jennings Bailey, notably in a Bailey Family Tree she is Thomas Alison "Alice" Jennings Bailey.

Her father was Thomas Jennings. My best guess for explaining her unusual name is that by the time she was born, her two older brothers named Thomas had both died. It was common to use a name again when a child died, and that her parents greatly desired to name a child Thomas after the father - so they gave her the legal name Thomas, calling her by "Alice" in daily life. She was their last child, so it worked out well for them!