“Barbecuedom” is the realm or sphere of barbecue; there can be “Texas barbecuedom” and “Tennessee babecuedom.” The word “barbecuedom” has been cited in print since at least 1989.
 
   
Google Books
The Best of New England
By Colleen Dunn Bates; et al.
New York, NY: Prentice Hall
1989
Pg. 64:
... photos of old Texas barbecue joints, a wall loaded with posters touting the finest of black Southern performers…all this leaves little doubt that Redbones of Somerville is an outpost of barbecuedom in the middle of Yankeeland.
 
9 March 1990, Orlando (FL) Sentinel, “Who has the best barbecue ? The drumroll, please…” by Scott Joseph, Calendar, g. 38:
1 is Arnold Bridges & Family Bar-b-que, 15518 County Road 455, Montverde, and it is the epitome of barbecuedom.
 
14 May 1991, St. Petersburg (FL) Times, “Barbecue’s a rib-tickler Series: OFF/BEAT” by Jan Glidewell, Citrus Times, pg. 1: ‎
Despite its roots in the traditions of the deep South, Hernando County is only lately coming into its own in the ranks of modern barbecuedom.
 
Google Books
John Madden’s Ultimate Tailgating
By John Madden with Peter Kaminsky
New York, NY: Viking
1998
Pg. ?:
Never in the history of barbecuedom has more food been cooked and eaten by so few people in such a short time.
   
Washington (DC) Post
The Grill and the Glory
By Steve Hendrix
Sunday, April 1, 2007
(...)
The master himself stands in a green camo windbreaker, accepting visits and tributes from his many admirers in barbecuedom.
   
Google Books
The Slaw and the Slow Cooked:
Culture and Barbecue in the Mid-South
Edited by James R. Veteto and Edward M. Maclin
Nashville, TN: Vanderbilt University Press
2011
Pg. 85:
In West Tennessee barbecuedom, the past is always linked to the present, in real and imagined ways; myth and memory are wrapped in whole-hog barbecue’s regional origins.
 
Eater
Here Is Texas Monthly’s 2013 Top 50 BBQ List, Unranked
Wednesday, May 15, 2013, by Paula Forbes
(...)
Check out the Top 50 below, and tune in tomorrow to find out whether Aaron Franklin’s cultishly-followed Franklin Barbecue in Austin gets the top honor in all of Texas Barbecuedom.