Since the census records for Mississippi show him born in Tennessee, I checked the 1860 census in Tennessee for Thomas. Can you verify his father's name? Here is a possibility:

Name: Thomas Dunn
Age: 24
Birth Year: abt 1836
Gender: Male
Birth Place: Tennessee
Home in 1860: District 6, Polk, Tennessee
Post Office: Springtown
Family Number: 718
Household Members:
Name Age
Percy Dunn 45
John Dunn 25
Thomas Dunn 24
Fanah Jane Dunn 22
Hannah Dunn 21
Samay Dunn 18
Margret Dunn 16
Lousay Dallis Dunn 12
Elijah Dunn 10

Can you verify a family match? This Thomas Dunn was most likely the same Thomas Dunn who enlisted as a private in Company D, 3rd Regiment Tennessee Volunteers (later 3rd Regiment, Tennessee Mounted Infantry [Lillard's]), in Benton, Tennessee, on May 6, 1861. Benton is about 15 miles from Springtown.