When the kid throws the cat into the dog show, the mob of dogs from "Foxy by Proxy" chases it out of the building.
Victor Barky (the Great Dane pianist) is a play on Victor Borge - perhaps as no surprise, one of Borge's nicknames was 'The Great Dane'.
In the Doberman Pinscher bit, the man named Doberman is Private Doberman from The Phil Silvers Show (aka Sgt. Bilko) which originally aired 1955-1959.
The animation during the sequence with Charlie Dog is traced from an earlier short, Often an Orphan (1949). Similarly, the Saint Bernard sequence recycles animation from Piker's Peak (1957).
The music heard when Laddy traverses the United States is heard in certain foreign language prints of The Scarlet Pumpernickel (1950).