Moshe, my suggestion would be to use a very large aperture to get a shallow depth of field. I have taken quite a few grab shots at dog parks, even one that was well received at a photography contest

Make sure you get all of the ears in and watch your composition.

Here are a few I grabbed at the dog park. None were posed. All were using a longer lens(50-200 which equals a 100-400 in 35mm terms) with a 2.8-3.5 aperture





The feet bug me in this one. I could always clone them out though



The first one I blurred the background further in PS and also warped it a bit so it made the cars unrecognizable. Minor issues with backgrounds can be fixed with PS. In focus ones are more difficult