I must say that while the idea of cobbling a dog seemed odd enough to catch my
softlink clicking fancy, I envisioned something relating to making
shoes suitable to the canine pediment.
I still have no idea what that might mean.
Webster 1913 is kind enough to explain that a coble is a type of fishing boat used around Yorkshire
That doesn't much help, either, does it?
BlueDragon is nice enough to point out that cobbler means testicle in cockney rhyming slang.
Ummm... yeah! Okay...
The mascot for Quavers, Colin, is a dog. It's not clear if the phrase is only used in reference to sufficient or excessive quantities of quavers. (Note: All I know about Colin and his Quavers I learned from the puzzle game Pushover published by Ocean Software.)
I also seem to have some strange untracable recollection that a dog is a template or workbench or guide of some sort used in the making of shoes by hand. "Dogs" is, of course, slang for one's feet.
Ah, now we seem to be getting some place.
So, you have enough to make a shoe. Why only one? This doesn't seem to mesh with the usage to denote a circumstance of surplus. Perhaps the original concept was correct: enough (leather) to make 4 shoes... for a dog no less, which would probably just chew them up in short order.