All I can think of is to shoot the scene on a tripod, but make sure you have just as much footage (in length) of the setting of the scene, but without the dog in it. Then, at the moment when you want to do the transporter effect, do a really slow fade from the footage of the dog to the footage of the same frame without the dog. Add the transporter sound to it. All this is missing is the blue swirly energy stuff...I'm not sure how to add that to the scene, but hopefully what I've told you makes some kind of sense.