Here is a fully workable dog rig I did:
You will see there is a root joint on the ground and a cog (center of gravity) joint in the middle of the spine, because I like it that way, rather than both as one joint. The spine extends in both directions from the middle, the shower-hook looking things above are IK handles, as is one for the tail, which is a separate chain, and one on the tongue. Each leg has an IK chain, and with sticky turned on, I can grab the hip handle and move the hips left and right, while the feet and forepart remain stable. By adding specific tail wag movements after that, I can get the effect you see when a dog wags its tail enthusiastically.
Missing from the picture is a look-at handle, because it is off-screen on the left. I use just a single point for both eyes, when you bring it in closer you get a crossed-eye effect, not as dramatic as in a Mel Brooks movie, but a more realistic look.
<* Wes *>