Firstly, they're not confined to one island - Quokkas are found on the mainland too.
And the reason they appear mangy and disease-ridden is because the tourists on Rottnest feed them, plus they raid rubbish bins. There was a population boom and now they survive in high densities on the island feeding on whatever they can scrounge, and disease is common.
However, the population on the mainland very healthy individuals.
Hey thats not nice quakka's are native to rotteness island just of Perth, been there a lot patted them and all its good to see them in there natural environment