Unless you both have all the gear and know how to move together Alpine Style on a ridge, a rope round a kid’s waist (or harness) is just false confidence. They’ll fall and just take you with them or the rope will rip out your hand, or it will snag and pull them off balance. Plus if you fall, they’re going with you…
Either they’re capable of doing it with close supervision and you keep the rope in the bag just in case you come across one section which is out of their depth; or you belay them the whole way.
EDIT: Closest I’ve come to being killed was moving together on a ridge in the Alps. We stopped to regroup and sort out gear on a huge platform (say 25 ton granite slab). My partner moved off and then as the rope went tight I started to move and as I pushed off the block, the whole thing vanished below me and fell 2000′ on to the Glacier below. We’d both been sat on it 5 minutes earlier chatting….