It is probable that Eliza was the daughter of Andrew (about 1760-1814) and Elizabeth (about 1768- before 1840) McKee.  Andrew made his will in 1805, but didn't die until 1814 (WP 21 Jun 1814).  That will included the following children:  
James (1791-1855), William (1789-1833), Edward (1798-bef 1847)and Andrew (1794-after 1847), Sally (abt 1790-bef 1847) , Mary ((abt 1803-bef 1860), Ann (abt 1804-bef 1850), Charity (1800-bef 1837), Jane (abt 1802- bef 1839) and Elizabeth (abt 1792- ?).  
Three more children were born between 1805 and 1814, according to the 1810 census.  On 15 Jan 1822, James McKee was named guardian of Jane and Eliza McKee, orphans of Andrew McKee ("Guardian Bonds Washington County, Virginia, 1780-1872," (1984), The Historical Society of WC VA Pub. Series II, No 21, pages 16 & 18).  So we can assume that Eliza was one of the three born after 1805.  To fit with the census numbers, her guardianship and marriage date, we can guess that she was born about 1806.

According to Alexander McKee's will (WP 22 July 1839), he is also a member of this family.  He names his brother James as executor, his sister Ann Speaks and her children, and the children of two deceased sisters -- Jinny (Jane) Jones and Rebecca Jamison.  This clearly places him in the family of Andrew and Elizabeth McKee.  So the three born after 1805 and before the 1810 census would be: 
Eliza (1806- ?), Rebecca (abt 1809-1839)and Alexander (1810-1839).

According to the Washington Co, VA, 1830 census, the Eleazer Rouse family consisted of 5 children:  1 male and 3 females under 5 and 1 female age 5-10.  They do not appear in the 1840 census.  So they could have died before 1840 or moved, as you say to Indiana.  What evidence is there that it was this Eleazer Rouse family that moved to Indiana?  I don't know anything about a second marriage for Eliza.

Hope this helps.

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