One of my favorite ways to take a picture of an animal (as long as I am close enough) is to zoom in on a particular characteristic, and them take the photograph with a shallow depth of field.
That is what I did here with my friend’s dog. I zoomed in tight on a single eye. Also fun are noses, tongues, and paws.
Being zoomed in the depth of field is generally fairly shallow, but if you can control the aperture, open it up wide so that all of the attention is focused where you want it.