The 1850 census shows:-

John Booker 1850 Male 52 White 1798 North Carolina 536
Caroline Booker 1850 Female 40 White 1810 South Carolina 536
John Booker 1850 Male 14 White 1836 Alabama 536
Willis Booker 1850 Male 13 White 1837 Alabama 536
William Booker 1850 Male 13 White 1837 Alabama 536
Rebecca Booker 1850 Female 11 White 1839 Alabama 536
Daniel Booker 1850 Male 9 White 1841 Alabama 536
Thomas Booker 1850 Male 8 White 1842 Alabama 536
Mary A Booker 1850 Female 1 White 1849 Louisiana 536

https://familysearch.org/ark:/61903/3:1:S3HT-D55Q-37F?wc=95R3-MJM%3A1031310701%2C1031598001%2C1031598002%3Fcc%3D1401638&cc=1401638

However these details do not tie in with the date and place of birth listed for Thomas Isaiah Booker on other sites where his birth date is listed as 1846 and place of birth as Louisiana. My guess is that the 1846 date is incorrect as that would make him only 16 in the photo and he would appear to be older than that, nearer the 20 years of age that the 1850 census would indicate.

Alan Thrower
England