Improving cognitive skills of young children has been suggested as a possible strategy for equalising opportunities across racial groups. Using data on four and five year olds in the Longitudinal Survey of Australian Children, we focus on two cognitive tests: the Peabody Picture Vocabulary Test, and the 'Who Am I?' test. We estimate the test score gap between Indigenous and non-Indigenous children to be about 0.3-0.4 standard deviations, suggesting that the typical Indigenous five year old has a similar test score to the typical non-Indigenous four year old. Between one-third and two-thirds of the Indigenous/non-Indigenous test score gap appears to be due to socio-economic differences, such as income and parental education. We review the literature on test score differences in Australia, and observe that our estimated gaps are lower than most of those found in the literature. This implies that the test score gap between Indigenous and non-Indigenous children may widen during school years, a finding that has implications for policies aimed at improving educational opportunities for Indigenous children.