A very large part of the increase in life expectancy at birth between 1800 and today results from the huge decrease in death rates of children under 6. So if you compared the life expectancies of six year olds in 1800 with the life expectancies of six year olds in 2000, the difference would be much smaller than the differences between life expectancies at birth in 1800 and 1900.
According to the National Center for Health Statistics, a child born in 1996 in the U.S. (either sex, any race) could expect to live 76.1 years (to 76.1) and a child six years old in 1996 could expect to live 70.8 years (to 76.8) – not much of a difference. In 1800, life expectancy at birth for Europeans (and probably for Europeans and person of European extraction living in the U.S.) was about 37 years. My SWAG would be that a European six years old in 1800 could expect to live about 50 more years, to about 56.
I couldn’t find any estimates of life expectancy at age six in the U.S. in 1800, but I did run across this estimate for ancient Romans:
life expectancy at birth, 25 years (to age 25)
life expectancy at age 5, 43 years (to age 48) http://www.utexas.edu/depts/classics/documents/Life.html