The second kanji, inu, just means dog. The first kanji is made up of two halves, both of which are kanji in their own right. If we take the kanji koma and split it into its two constituent parts, we get:
Now, the left hand kanji is uma, which means 'horse', but it also sort of means 'stupid' - it is used in the word baka which means 'stupid'. The right hand kanji means 'phrase' or 'sentance', and also is a counter word for haiku. Putting these characters together gives us:
Now, as you may know, kanji in Japanese have several different readings, usually a Japanese-style and a Chinese-style. Interestingly, the above characters can also be read pa gu inu or 'pug dog' in the Chinese style. Our little trail leads us to the fact that the characters for temple dogs, if seperated, can be read as 'pug', and have the meaning of 'stupid dog'. Coincidence? I think not...