MC, I'd respectfully suggest that this wasn't cloning for the sake of science...I think this was someone doing this because they couldn't deal with their grief. (As for cloning for science, that's a whole other can of worms, but I don't want to open it right now.)
One of the aspects that bothers me is, I almost think it dishonors the creature that has died, by acting as if he or she can be replicated or resurrected by humans from the dead. I imagine most people would react with revulsion at the idea of doing something like this with a person. A cloned animal might have the same DNA, but there are other factors even on the physical level that differ--factors affected by environment and nurture, which cannot ever be exactly the same between the original and the clone. Plus, many clones become sick and die. Some age more rapidly than normal animals. I don't understand how I could knowingly have a creature created simply because I could not deal with grief--and run a high risk of subjecting him or her to that sort of torture just because I could not face a natural part of life.
On no level can we create the same creature twice. And I know not everyone will agree with this, too, but I think that the worst thing about it is, the new animal has a new soul, that thing that we cannot create ourselves. Yet to expect him or her to be the same creature is somehow very wrong. I speak as someone who has had cats and dogs, and currently has a cat...and I could not ever attempt to clone one of them. I feel like it would dishonor their lives and their uniqueness. I even say this after having acompanied and soothed my old cat as she was put to sleep, because I couldn't turn my back on her then. It was terribly hard...I was crying...but I truly feel like the right thing was to let her go and keep the memories. And I know not everyone feels that animals have souls, but I honestly believe that grieving and letting her go was the way to honor all that she was.