Border
Since this looks like a large picture of Butch, very nice quilt, very cute pooch, I like your idea of the picture frame. Suggestion - make a line about 1/4" out. Then another about 1/2" then a third 1 1/2". You may have to change that 1 1/2 - to 1 1/4. If your 2 1/2 was without seam allowance. You need to keep away from the binding a bit since the judges also take off if your quilting ends up going into and under the binding.
After you make all your trips around that border. Go back and fill in the space between the first and second lines. Tiny little circles works good for that. This will give you the beading look that frames have. Take a look around your house at real frames and you will see what I mean. The fabric you are working on doesn't appear to be one that will show tiny paw prints as you mentioned, which is why I vote for the frame idea.
Happy Stitching