In the movie, Alpha's high-pitched voice is a surprise to all the dogs. In the short, which takes place before Dug's first scene in the movie, Alpha's voice is already high-pitched.
Alpha: [speaking in a high-pitched broken collar voice to Dug, who is in a hole in the ground]
This is the bird's favorite hole. Under no circumstances are you permitted to SQUIRREL!
If we consider the day that Carl gets out of bed to his alarm clock "Day One" of the feature film Up, Dug's Special Mission takes place on Day Two, shortly before Dug meets Carl and Russell.