Just adding my thoughts to Catharina's - I used a waterproof crib pad (the size of a crib mattress but with no overhang - between layers of fitted sheets. You might have something like that left over from when your daughter was in the crib. It was great. The mattress pad and the bottom fitted sheet stayed dry. If the top sheet got wet, I just stripped it and my child slept with the blanket against his skin.
But yes, put her back in the pull up. Why not? She's not sleeping, and neither are you. The couch is going to be a bad habit, you're right. She's not ready - it has nothing to do with training - it has to do with the full bladder giving the signal to the brain to "wake up". It's neurological, not behavioral. My son was WAY older than this when he stayed dry at night.