Considering the things people will eat in Iceland, I don't think you'll find a ton of organizations that are promoting animal rights.  Add the fact that most global conservation organizations have campaigns actively targeting Iceland, and you're 0 for 2.

However, if you're interested in something like this, why not reach out to http://www.ust.is/the-environment-agency-of-iceland/ and see if they partner with anyone.

Also, the team members native to the area might have some ideas.

-Fuse