Is my reasoning about "could have done otherwise " being unnecessary for moral responsibility sound?

Let's say I live in a universe where I have the ability to do otherwise. Let's call it "CDO", and let's say I'm presented with the opportunity to kill a dog, and on doing so be rewarded with ten thousand dollars. Now, I have the ability to do otherwise, yet everything about me, about my character is opposed to hurting animals, no matter the reward on offer. My upbringing, education, culture, experiences etc have shaped me into the sort of person who just never do such a thing. I logically and morally can't commit such an act. I can't do otherwise.

Now, why am I not morally responsible for my actions in the way the libertarian wants? I grant them that in some metaphysical sense I could do otherwise, the universe is not deterministic etc yet I can't, I can do no other, reason and my morals and character compel me. There is no alternative. Why would I be less morally responsible? I just don't understand what "CDO" does to add to my responsibility in anyway that I should care about.