There are any number of places you could choose to create portraits of cats and dogs for their adoption ads. There is usually more light outdoors if you can find a quiet spot without a distracting background — and if you’re photographing dark colored dogs you need all the light you can get! You should look for a bright shady spot away from other dogs, bicycles and noisey traffic–all things that are way more interesting to your subject that you are. If you want him to look at the camera (and you do) then isolate him from distractions.
Choose the background carefully (how about a hedge or a brick wall ?) and then face your subject towards the light. In other words, shoot IN TO the shade, don’t stand in the shade and have the bright sun behind your subject. Get down on his eye level (yes, this involves bending at the knees and getting on the ground. It’s worth it) and surprise him with one sharp crazy noise — he’ll look right at you — and you’ll create a photograph that will reach out and grab someone’s attention.