Quokka Fact: 7. Quokkas sleep with their heads down Humans and quokkas position themselves quite differently when it comes to nap time. When quokkas want to catch a few Z's, they sometimes nap with their head bowed down, rested, at their feet. As nocturnal creatures, they primarily rest under shade throughout the day. The best times to see quokkas moving about are early mornings and late afternoons.