It depends on how much you remember. If you have a good memory of the main plot and characters, the chances are quite high. You can use your recollection as a guide to rewrite it.
Well, you could try to piece it together. Maybe your dog didn't completely destroy it. Check if there are any chewed - up pages that still have legible parts. And if you can't find any remnants, think about the overall story arc in your head. You know, like how it began, the main conflict, and how you intended it to end. Then start writing again.