There is no direct animal predators but human impact on the environment can cause a threat to their lives. In the 1930's Red Foxes came to Australia with European settlers and would hunt them. Since males that weigh more are the dominate males they have a higher chance to reproduce and survive
Since quokkas are a primary consumer they are indirectly in competion with other primary consumers like koalas. Within their own species they can compete over fighting mates.
The quokka is recognise as a threated species and thei vulnarble. They are describes as fauna meaning likely to become extinct. Their population is decreasing, In 2020 they were only 10,000 adult individuals.
Everything we are doing to their environment is harming them, such as pollution, buliding more houses and buliding in their environment. Wild fires created by environmental changes can also affect the quokkas. If we dont start changing our ways about their environment their population will stay decreasing. All enviromnental changes like recycling and not buliding near where they live.