How did a dog's breakfast get such a bad reputation? in the 1937 Dictionary of Slang and Unconventional English, the expression is listed as "a mess." It is suggested that this dates from before the time of canned dog food when a dog's breakfast consisted of dinner leftovers from the night before.
This should not be confused with "a dog's dinner" which means the opposite and is normally expressed as "all dressed up like a dog's dinner" and sarcastically means over-dressed or showy. This comes from makingheadsortailsofidioms.com where the list of expressions is quite fun.
More on the dog's dinner from a New York Times article ON LANGUAGE: Dog's Breakfast: "Why have you got those roses in your hair?" asked a character in "Touch Wood," a 1934 novel by C. L. Anthony. "You look like the dog's dinner ." This expression was defined by the Oxford English Dictionary Supplement as "dressed or arranged in an ostentatiously smart or flashy manner," probably derived from the 1871 usage "to put on the dog ." And lest we forget, the New York Times examines the well-worn expression - 'dog-eared.'
I found this picture of Dezi on a spring search under the wisteria. Is it for a dog's breakfast or a dog's dinner?