The U.S. Census of 1850 , 1880, and the Michigan State Census of 1894 all give the age of Julia Ann which calculates to a birth year of 1805. However, the U.S. Census of 1860 gives an age which calculates 1804 as her birth year.
At one time, a source was found which allowed her birth month to be calculated as February 1805. However when citing for this source, this information source could not be found again. It was thought this "lost" source was fairly reliable.
Also at one time, some information was found which suggested a birth date of 5 to 7 February, but again this "source" has been lost. It was thought to be only a possible date at best in the month of February.
Thus, the only fairly reliable information is the 1805 birth year from the three censuses. If the "lost" information resurfaces, I will change her birthdate to include month and day.