Cool, now I have to see that. The costume and the shape-shifting aspect reminds me a lot of The Invasion of the Body Snatchers, (all 3 versions) which I liked a lot. (My favorite one is the 1970s one set in San Francisco.. )
Here is a scene from The Thing. No dogs in it, though, unfortunately.
seems at the beginning there is a dog scene
ahh.. here is a synopsis which explains the dog costume.