A dog won't be any "safer" in a tent from a mountain lion or bear than you would. Two of mine don't wander of while I'm sleeping and one does. The one that does is on a long leash, and I keep it wrapped around my wrist or arm.
If your dogs sleep close to you at home, they'll sleep close to you in the woods.
If you have a big enough tarp, I don't see any reason to have another cover just for the dog. Also, sleeping on a ground cloth on top of duff is going to be just as plush as laying on the carpet in my house if not more. Heck, they lay on a concrete patio sometimes. Why would they need their own hammock?
All dogs are different. Mine has a thin coat, and when he gets cold he pokes me with his nose and tries to get into the hammock. Some dogs bark at every little sound or smell in the night, but rest more quietly in a tent. I keep mine on a long leash at night, usually tied to one of the hammock trees. I often tie tarp and hammock out to trees on each side instead of stakes so there will be lees likelihood of the leash getting tangled around guy-lines.