It means that this person is lacking in intelligence/simple-minded, with the suggestion that he may also have slight mental problems. The clue is in the word 'Slow' and it's also in the reference to the dog, who is 'as daft as Lucky is'. In British English we have many expressions along the lines of 'a penny short of a pound' which are euphemisms for mental deficiency. 'Not a full shilling' is one, also related to money, and there are many others, such as 'a few sandwiches short of a picnic', which suggest that the person in question may not have a full complement of working brain cells. These expressions are rather politically incorrect, but can be amusing and imaginative.

Meaning not very smart. Also... A sandwich short of a picnic. Not the sharpest knife in the drawer. A few cards short of a full deck. etc,etc.

"A penny short of a pound" means that Slow-and-lucky is stupid, or not very intelligent in some way. So you could also write: "Slow-and-lucky, who is stupid...". The word "daft" at the end of the sentence also means "stupid". I hope I could help :)