Modelling disease dynamics is most useful when data are limited. We present a spatial transmission model for the spread of canine rabies in the currently rabies-free wild dog population of Australia. The introduction of a sub-clinically infected dog from Indonesia is a distinct possibility, as is the spillover infection of wild dogs. Ranges for parameters were estimated from the literature and expert opinion, or set to span an order of magnitude. Rabies was judged to have spread spatially if a new infectious case appeared 120 km from the index case. We found 21% of initial value settings resulted in canine rabies spreading 120km, and on doing so at a median speed of 67 km/year. Parameters governing dog movements and behaviour, around which there is a paucity of knowledge, explained most of the variance in model outcomes. Dog density, especially when interactions with other parameters were included, explained some of the variance in whether rabies spread 120km, but dog demography (mean lifespan and mean replacement period) had minimal impact. These results provide a clear research direction if Australia is to improve its preparedness for rabies