Dingoes come from an ancient canid lineage that originated in East Asia around 8000-11,000 years BP. As Australia's largest terrestrial predator, dingoes play an important ecological role. A small population exists on a world heritage listed offshore island, K'gari (formerly Fraser Island). While dingoes on K'gari are protected, dingoes on the mainland are only protected in certain regions, and, because of its controversial status in Australia, lethal control is commonly used for management. Concern regarding the persistence of dingoes on K'gari has risen due to their low genetic diversity and elevated inbreeding levels. However, whole-genome sequencing data is lacking from this population. Here, we include five new whole-genome sequences of K'gari dingoes. We analyze a total of 18 whole genome sequences of dingoes sampled from mainland Australia and K'gari to assess the genomic consequences of their demographic histories. Long (>1 Mb) runs of homozygosity (ROH) --- indicators of inbreeding --- are elevated in all sampled dingoes. However, K'gari dingoes showed significantly higher levels of very long ROH (>5 Mb), providing genomic evidence for small population size, isolation, inbreeding, and a strong founder effect. Our results suggest that, despite current levels of inbreeding, the K'gari population is purging strongly deleterious mutations, which, in the absence of further reductions in population size, may facilitate the persistence of small populations despite low genetic diversity and isolation. However, there is little to no purging of mildly deleterious alleles, which may have important long-term consequences, and should be considered by conservation and management programs.