The easiest method to determine 'White Dorothy' is to look for it to sport back and forth from white to pink. Another marker for both Dorothies is to look at the new growth. It is generally a "bronze" color. The flower in the photo doesn't look dark enough pink to be pink 'Dorothy Perkins'. I don't recall seeing varying shades of white to pink. I think they are generally either white or bubblegum pink. Finally, check out the pedicels; the Dorothies might have a few tiny hairs, but never a profusion of bristles.