I came across this bit of intelligence, believe this may be your William who wound up in Louisiana and featured in the 1860 census there. Nothing further.

Francis Marion Grubbs, Jr. b. 1797 Ga. d. 1875 Rials Creek - Simpson Co. Ms.
m.1st 1819 Feliciana Parish, La. Susan Sanders b.1797 d.1833 Rial Creek. Their son William F. Grubbs m. Caroline Gartman of Pike Co. Ms.

F.M.G.,Jr. m. 2nd Mourning Brown b.1821 d. bef.1870.
Burial: Home Place at Rials Creek near where Peacock and Main St.South cross.

Two Sons: Francis Marion Grubbs b. 1838 and James Marion Grubbs b.1842.

I have more information but to much to type. Plus I am Looking for lots more. I can be contacted at:
dickiegrubbs@hotmail.com
or 502 11th.Ave.North
Onakaska,Wi.54650
or 1-608-783-4820.

https://www.ancestry.com/boards/thread.aspx?mv=flat&m=193&p=localities.northam.usa.states.mississippi.counties.simpson

………..

1860 United States Federal Census

Name: William Grubbs
Age: 36
Birth Year: abt 1824
Gender: Male
Birth Place: Mississippi
Home in 1860: Ward 6, Bossier, Louisiana
Post Office: Orchard Grove
Household Members:
Name Age
William Grubbs 36
Carline Grubbs 35
Gilbert Grubbs 11
Mary Grubbs 8
Silvus Grubbs 4
William Grubbs 3
Jane Grubbs 2
Robert Grubbs 10/12
Charls Grubbs 60