In my case, no...for two reasons.
First, you can never be 100% sure you have the right person (especially given a lengthy history of police falsifying evidence, etc., and there can always be other factors involved). If you incorrectly put someone in jail you can attempt to make amends later, but how do you make amends to a person you murdered?
Second, given how human beings have evolved and how their brains function, life in solitary would be a far worse punishment if the goal is to punish or make them suffer for their crime. If your goal isn't punishment or reform, but instead simple revenge, then I suppose this argument wouldn't carry much weight for you.
This seems like a classic "Either/or" logical fallacy.
Related to your dog example (from what I've read over the years), execution is not more cost effective than permanent confinement. In human society, this is mostly due to the legal costs of running a capital sentence through a lengthy appeals process.
Your original post did not mention cost effectiveness, it just asked about support for a death penalty. Regardless of cost, my stance is in the last paragraph of my original post: that permanent confinement is a more suitable punishment.