Providing you are physically able to do so, wouldn't it be easier and more accurate to just assume a prone position using your elbows for yourself and camera support. You can then use either the viewfinder or live view for proper framing, focus, etc. It might even be a good conversation starter when dog owners see how serious you are at taking pictures of their pets .
The only caveats would be to wear "casual" clothing, and look carefully for doggy residue before laying down .
Edited to add: You haven't filled in your "equipment profile" yet, but if you have a tripod with a head adjusted to a sitting height that would give you a good (low) perspective and be better than both the options above. Holding your camera at knee-level as you described and expecting good results doesn't sound like you would have many "keepers".