I'm inclined to accept Shannon Elder's 1938 list of the 15 children of David Elder, which doesn't include a son David Jr. As a consequence, I think one should look elsewhere for the answer this query.
David Sr. had a brother John who apparently had a son David:
Georgia intestate records
By Jeannette Holland Austin
[Available via Google Books]
ELDER, John, decd, Richard Cox, gdn of Jack, Jerry, Joseph, DAVID and Doctor Washington Patrick Henry Elder (sic), orphs, 9/7/1812, David Holmes, Sterling Elder, surs, Clarke, GB (Guardians Bond)
What about "Junior" in the 1830 Census?
1830 United States Federal Census -- Ancestry.com
Name:David Elder Junior
Home in 1830: Clarke, Georgia
Free White Persons - Males - Under 5: 2
Free White Persons - Males - 20 thru 29: 1
Free White Persons - Females - 5 thru 9: 1
Free White Persons - Females - 20 thru 29: 1
1830 U S Census: Clarke, Georgia, Page: 317; NARA Roll: M19-16; Family History Film: 0007036.
Junior doesn't always mean "son of" - can mean "the younger". For example, in the 1818 Tax Digest of Clarke County, Joshua Elder Jr., Joshua Elder Sr. and David Elder Sr. are listed [Abbe, Clarke County, Georgia, Tax Digests, 1811-1820, 2005, page 308]. Joshua Junior was "the younger", nephew of Joshua Senior and son of David Sr.
John Elder is last found in Virginia records in 1807 [Henry County, Virginia, Personal Property Tax records, Microfilm reel 175, 1782-1830, Library of Virginia], so a David born about 1801 in Virginia could be his son.
John Elder married Ann Johns in Charlotte County, Virginia, in 1799 [Virginia Marriages to 1800, Ancestry.com]. An Ann Elder appears in the 1820 Census with 4 boys:
1820 United States Federal Census -- Ancestry.com
Enumeration Date:August 7, 1820
Free White Males - 10 thru 15: 1
Free White Males - 16 thru 18: 1
Free White Males - 16 thru 25: 3 [2 - 19-25]
Free White Females - 45 and over: 1
1820 U S Census: Salem, Clarke, Georgia, Page: 147; NARA Roll: M33_8; Image: 102.
A David born in 1801 could be living with her.
Lastly, the 1828 Tax Digest of Clark County lists David Elder Jr., Jerimiah Elder and Nancy Elder together in Capt. Atkinson’s District [Abbe, Clark County, Georgia, Tax Digests, 1821-1830, 2005, page 376]. Jeremiah was son of John Elder deceased; Nancy probably was Ann, John’s widow. David Elder and several sons (including Joshua Jr.) are listed in Capt. Simm’s District (Abbe, page 394).
The following web page has more information on John Elder and family: