I'm not related but am familiar with the area. Looks like they lived on the Cecil County, MD side of the canal in 1850 and John is buried on the Delaware side. Eliza is shown as age 11 in 1850 - seems reasonable that she's the person you're researching. Her siblings William, Susan and John are mentioned in a cemetery memorial, as well as an Isaac, who is not listed in the 1850 Census.
As usual, dates are inconsistent between records but, they provide leads. Eliza J. Giberson b. 1839 in MD to John Giberson and Rebecca W. Muffet Giberson might actually lead somewhere. Take a look at the cemetery memorial link: http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=55638502http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=55638502