I would encourage you to take the time to just consider this in a different way. Animals that are loved are soulish, the incredible (but unfortunately not Catholic) Dr. Hugh Ross makes this easy to understand: http://www.reasons.org/articles/origin-of-soulish-animals. I would simply add that God allows us to form loving bonds with animals to provide a little heaven on earth --a loved [animal of your choice] is heaven on earth. But heaven being heaven, we won't need something as wonderful as our animal friends to make existence better.

Now if the misguided Puritans didn't have their way everybody would be able to die with the amount of dignity they need to make it to the end of the race. Why, because God has provided us with all the tools we need to control pain, but the powers-that-be (really they are the pain-givers either intentionally or just out of ignorance) deny this to us --think about all the places that put people in jail for growing a plant, or otherwise prohibiting scientists to their jobs to make things better.

My inner St Francis tells me that we euthanize animals at the correct time because of our love and respect for them, and there's no consequence for their souls. But for our fellow man, we provide care to its natural end so that we can all live forever.

Frank T. McAndrew did a great job with this article. I think about this stuff all the time because for me it's infinitely interesting, but in my case, I put a Catholic spin on it.