This phrase pre-dates the nickname "Trolley Dodgers" and was not original to Brooklyn.
The only Brooklyn World Series title came in 1955. Rebuilt into a contending club first by Larry MacPhail and then the legendary Branch Rickey, the Dodgers won pennants in 1941, 1947, 1949, 1952, and 1953. In all five of those World Series, however, they proved unable to overcome the New York Yankees. Then, in 1955, the long-cried slogan "Wait 'till next year" became "This year is next year!"
7 March 1938, New York Times, pg. 22:
So in the words of Brooklyn Dodger fans from time immemorial, the miracle worker, Waters, can say, "Wait until next year."
14 July 1940, Lima (Ohio) News, pg. 12, col. 3:
NO LONGER DOES "WAIT TILL NEXT YEAR" RING THROUGHOUT BROOKLYN, WHERE EVERYBODY FROM THE BOROUGH PRESIDENT TO THE BOOTBLACK IS CONVINCED LEO DUROCHER WILL TAKE THE DODGERS ALL THE WAY THIS SEASON.
2 October 1941, Washington Post, pg. 27:
The eternal slogan of the Brooklyn Dodgers, "wait'll next year," was altered today to "wait'll tomorrow."