I rely quite extensively on my speedlights for puppy photos, (YN-560 III & IV). I usually just use one on camera, and bounce it off the ceiling for nice even light. It’s amazing how flash brings out the details. It just gives a little “pop” that you don’t get without a flash.
Of course you’ll have a different set of headaches, like reflections, and various other problems, but for me, I would sooner go without lunch than try puppy pictures without flash. 🙂
Of course when I’m outdoors, I don’t usually need the flash, but indoors it’s a must.