Rabbits are very much homebodies and OCD.Rabbits do. I think they'd close the door if you forgot to, haha.
I had a pet rat who got out of her cage every night, went out for adventures, and then got back in her cage and closed the door by morning. It took me a good long time to figure that out.
I have a hamster now but I don't think hamsters are as smart as rats. Too inbred probably . But she does lunge at the side of the cage when a cat gets too close so I don't think she'd be easy prey.