Chris Smithson has been helpful once again. He found a marriage announcement for Elizabeth George in The Baltimore Sun.
It mentions her as being from Middlesex County, Virginia. She married William Mooney on June 11, 1856 in Baltimore. The announcement was published in the July 8, 1856 edition of the paper.
This Elizabeth — Elizabeth George Mooney — is likely the daughter of Elizabeth George, sister of Wesley, who was living with her mother and brother in 1850. According to the 1850 census for Baltimore, Elizabeth was 11 years old at the time. Therefore, she was born in 1838 or 1839.
Middlesex County, Virginia is across the water from Lancaster County, Virginia where the elder Elizabeth was born in about 1806.
Two researchers of the George surname — Gaybrooke Crittenden and Karen Wallace — are listed on the “Middlesex County Surnames Register” but neither of the email addresses provided work. Hopefully I will be able to track them down (and other researchers) to help fill out the family tree.