Well .. killing any life has a certain karma associated with it. No animal is holy or dirty for that matter. All life has a certain sanctity. However, we do not treat a rock and a flower in the same way in the social sense!
A cow is known to exhibit human-like emotions of joy, tears & pain according to how people act with it. And in India, lot of children grow up drinking cow's milk, especially in rural India. So, it is considered like killing a human if one kills a cow.
A dog is also a man's friend but sometimes acts violently. So, people have generally kept them at a certain distance (though that is all changing nowadays).
Let's first see how the principle of Karma works. It is not just about action, but also about volition. If you think of doing a violent act, and not actually do it, you still acquire the karma because what we do physically in the world is just an outwardly manifestation of what we think in our mind. Thought precedes action and every action has a consequence.
Karma is so feared because of the impact it is supposed to have on a human being. Most people are ok with taking an action but do not want to deal with the consequence.
Now, if you are killing a human being, do you acquire a bigger karma than killing an animal? Most people would argue yes. But bring in the context that the human is a terrorist trying to kill you & your family whereas the animal is a cow or a dog you are lovingly bringing up. What happens in that case? The equation reverses for most people. Karma does not work like that.
It is actually about how we are while thinking or performing the action! If one is in awareness, of life and consequences of every action one performs, one is said to be free from Karma. This can be considered as the essence of Bhagavat Gita.
So, the answer to "do you get more Karma while killing a cow than while killing a dog?" is - 'It Depends'! It depends entirely on how the volition & action happens within you. If you are acting utterly out of cruelty (knowingly or unknowingly), killing any animal or human will get you lot of Karmic burden.
You may also want to read this to get an idea of how in Sanatana Dharma, a butcher could become a Guru for a monk: https://en.wikipedia.org/wiki/Vyadha_Gita