Dogs are mentioned in the Bible 14 times. Cat isn't mentioned at all.
The only dog mentioned by breed in the Bible is the greyhound:
There be three things which go well, yea,
Which are comely in going;
A lion, which is strongest among beasts and
Turneth not away from any;
A he-goat also. (Proverbs 30:29-31, King James Version)
In the Bible, dogs are considered ill-tempered scavengers that are tolerated, but not loved. (Source) (Photo: Neurodoc [wikipedia])