Yes, it's normal for them to want to move their kittens. You are right, under the couch is a BAD place to have them. She is probably confused and isn't doing the best job right now. You can help her by getting her settled with her babies in a warm place. The kittens MUST be kept together and warm as they can't generate their own body heat as newborns. I would get a box or a new jumbo covered litter box and put some towels in the bottom. Clear out the floor in a closet in a quiet room and move the nursery in there. for warmth, you can put a heating pad UNDER about half of the box so the kittens can get warm, but there is room for mom to move off of the heating pad if she gets too warm. Jumbo litter boxes make great nests for cats, and the box comes in handy when your done with kittens and need a new litter box. She may move the kittens around again. Keep the bedding changed every few days, as dirty bedding is one of the cues for them to move the babies. Keep her confined with her kittens to the quiet room until their eyes are open and they are moving around the nest pretty well. At that time, you can remove the heating pad also. Please let me know if I can help further. Your girl can be spayed once the kittens are eating solid food on their own. I suggest waiting until then in case she decides not to feed them any more after the surgery, they will do fine without nursing. Congrats on your new family!

__________________
Please Press ACCEPT if my answer helped solve your problem.
Lori McLaughlin
Your veterinarian should ALWAYS be consulted first and foremost when your pet's welfare is at stake.