"Big D" has been cited in print since at least the early 1930s.
Dallas (/ˈdæləs/) is a major city in Texas and is the largest urban center of the fourth most populous metropolitan area in the United States. The city proper ranks ninth in the U.S. and third in Texas after Houston and San Antonio. The city's prominence arose from its historical importance as a center for the oil and cotton industries, and its position along numerous railroad lines. The bulk of the city is in Dallas County, of which it is the county seat; however, sections of the city are located in Collin, Denton, Kaufman, and Rockwall counties. According to the 2010 United States Census, the city had a population of 1,197,816. The United States Census Bureau's estimate for the city's population increased to 1,281,047, as of 2014.
The city is the largest economic center of the 12-county Dallas–Fort Worth–Arlington metropolitan area (commonly referred to as DFW), which had a population of 6,954,330 as of July 1, 2014, representing growth in excess of 528,000 people since the 2010 census. In 2014, the metropolitan economy surpassed Washington, DC to become the fifth largest in the United States, with a 2014 real GDP over $504 billion.
Wikipedia: Big D (song)
"Big D" is a song about Dallas, Texas written by Frank Loesser in 1956 for the musical The Most Happy Fella. It repeatedly spells out the name of Dallas with the refrain: Big D, little A, double L, A, S.
17 August 1933, Dallas (TX) Morning News, section I, pg. 5:
He came right into the big middle of Big D for Dallas and using a high-powered explosive (all explosives are high-powered) he blew up the jail.
the true story of Clyde Barrow and Bonnie Parker, as told by Bonnie's mother (Mrs. Emma Parker) and Clyde's sister (Nell Barrow Cowan)
compiled, arranged and edited by
Jan I. Fortune
Dallas: The Ranger press, inc.
Pg. 73: I'll jump right up and start towards Big D.
11 October 1937, Austin (TX) Statesman, "Everyone Turns Out For Dallas Whirl," pg. 3, col. 1:
AUSTIN moved in a body to Dallas over the week-end to participate in that annual verve in all the O. U.-Texas activities. From kicking that football to kicking their heels in attempts at terspsicorean fantasies, Austin went round and round with the great throngs crowding Big D.
February 1946, American Speech, pg. 31:
Big D, n. Dallas.
19 August 1954, New York (NY) Times, pg. 27 ad for Sports Illustrated:
...and both Neiman-Marcus and A. Harris & Co. in Dallas who devoted some of their Friday newspaper ads to telling the folks in Big D about our magazine...