Yes, move the babies. Check to make sure they are all alive and un-injured and that there are no placentas left in with them.
Make a nest if she has not already made one from hay. Stuff a box (shoe box, dish bin, clean litter box) with hay until it is fairly tightly compacted, and make a hole in the middle. You can put some shavings or bunny save litter on the bottom of the box before filling with hay. I would avoid putting a towel or blanket in the box unless it is fleece. I've heard of too many horror stories about finding baby bunnies tangle in strings that have come loose and loosing limbs or strangling to death.
Move any fur and nesting material that she has put together into the nest you have made for her. You can gently pluck some hair from her belly or under her chin as hormones should cause that fur to become very loose.
The babies should be nice and warm, wiggly and jump and squeak if you put your hand over them in the nest. Their bellies should look round and if mom is feeding them really well, you may be able to see the milk in their bellies.
-Dawn