This paper analyzes the mobility of low income mothers in Australia between two groups of governmental transfer payments: Income support payments (IS) and Family Payments (FP, non-income support payments) only. While IS payments are to provide a subsistence of living for her, FP payments are to help low-medium income families with the costs of dependent children. We use a dynamic multinomial logit panel data model with random effects, explaining the reliance of each individual on the income support system during each quarter between 1997 and 2000. The data is drawn from the FaCS 1% Longitudinal Data Set (LDS), a sample of fortnightly administrative records of welfare payments in Australia. We find that both state dependence and unobserved heterogeneity play significant roles. We also find that single mothers and females with partners on income support payments are much more likely to be on income support than otherwise.