yep, you NEED a tripod for this.
shoot the dog. Not like that. Shoot the dog doing whatever you want it to, then fix the tripod on it. don't move the tripod. get the dog to stay there for as long as you want the transporting wibbly wobbly bit to last. then throw something at the dog. get it to run away. get a second of that shot.
Then, like above, you just have to add some wibbly wobbly effects over the dog, and do a fade or something to the new scene. the bits of the dog will be replaced by what's behind it. I dunno what the effect is called. might just work with a fade.
i realise this post is similar to what's said above, but there's more animal cruelty in mine.