Polyploidy has played an important role in evolution across the tree of life but it is still unclear how polyploid lineages may persist after their initial formation. While both common and well-studied in plants, polyploidy is rare in animals and generally less understood. The Australian burrowing frog genus Neobatrachus is comprised of six diploid and three polyploid species and offers a powerful animal polyploid model system. We generated exome-capture sequence data from 87 individuals representing all nine species of Neobatrachus to investigate species-level relationships, the origin and inheritance mode of polyploid species, and the population genomic effects of polyploidy on genus-wide demography. We describe rapid speciation of diploid Neobatrachus species and show that the three independently originated polyploid species have tetrasomic or mixed inheritance. We document higher genetic diversity in tetraploids, resulting from widespread gene flow between the tetraploids, asymmetric inter-ploidy gene flow directed from sympatric diploids to tetraploids, and isolation of diploid species from each other. We also constructed models of ecologically suitable areas for each species to investigate the impact of climate on differing ploidy levels. These models suggest substantial change in suitable areas compared to past climate, which correspond to population genomic estimates of demographic histories. We propose that Neobatrachus diploids may be suffering the early genomic impacts of climate-induced habitat loss, while tetraploids appear to be avoiding this fate, possibly due to widespread gene flow. Finally, we demonstrate that Neobatrachus is an attractive model to study the effects of ploidy on the evolution of adaptation in animals.