Do dogs have small brains

Compared to, say, a human? Sure, a dog's brain is smaller than a human's. But then, a human's brain is smaller than a whale's brain, so it's all relative. If you mean 'are dogs stupid,' then it depends on the breed. Some breeds (like Afghan hounds) are rather notoriously dumb, while others, like Pembroke Welsh Corgis and Border Collies, are incredibly intelligent. Also size doesn't necessarily matter the elephant has the same mass as our brain but yet it's larger in size because ours is more compact then theirs.