Is this herbicide toxic to animals?

I assume your use of quotation marks around the word organic implies that you realize there's nothing organic about MCPA. While it's not the nastiest option, it's by no means an organic product. Definitely a good idea to keep the dogs off the lawn for a few days. As far as the ducks, it could be a little more harmful to them so you're right to keep them from eating the seed. Maybe you could clean it up before the MCPA is applied next time or at least clean it up after and put out fresh seed a few days after the application. Check out the Pesticide Information Profile from Cornell University or contact your county extension office for more information.