Yes. Wisdom Panel is designed for dogs of all ages and is safe and easy to use at any stage in a dog's life. However, Wisdom Panel does recommend waiting until a puppy has been weaned to prevent cross-contamination from suckling on their mother and having cells from her skin and milk in their mouth at the time of swabbing.
Note that it can be very difficult to observe breed traits in puppies, because they are growing and developing rapidly. Most dogs will not achieve their final mature physical traits until they are at least one to two years of age.