I totally second Bitter's comments, a photographic style is something that really one has to almost fall into rather than try to force out' at least that is the pattern for many. The other method is finding another style that you like and learning to emulate it (which in turn teaches you new skills and will also, over time, change into your own take on the style itself).
Best thing you can do is to always keep your mind open to new interpretations, opinions and methods (both in camera and in editing) - learning and having diversity of skills is a big thing that helps you develop, mature and choose a style to shoot
As for the shot you might find that burning some of the select areas of the whites on the dogs face might well help as these appear to have or be very close to blowing out. If you shoot in RAW chances are the details are still there to be recovered and you can duel process the RAW - once for normal and once for the whites alone - and then merge the results manually with layermasks in editing.