Can damage taken from the In Need of Rest treachery card in The Dunland Trap?

I know in a lot of their games FFG is very particular about their wording and In Need of Rest says that attached hero "takes" 1 damage rather than is "dealt" one damage.

Would card like Loyal Hound that cancel damage dealt to a hero cancel the damage taken?

Yes, you're fine to cancel it. For whatever reason, phrasing around damage effects has always been a little loose in this game, and there are still some unsolved issues out there. But I think this one is fine.