No. A refugee who has permanent residency in Australia receives exactly the same social security benefits as any Australian resident in the same circumstances.
A single person with no dependent children who is eligible for the Newstart Allowance (whether or not he or she is a refugee) will receive up to $559.00 per fortnight, whereas a single person on an Age Pension payment will receive a fortnightly payment of up to $850.40. A single age pensioner therefore receives over $200.00 more per fortnight more than a single refugee (or a single Australian citizen or permanent resident) who qualifies for the Newstart Allowance.
Australian citizens and permanent residents with dependent children on lower to middle incomes (including refugees) may also be eligible to receive Family Tax Benefits or Parenting Payments. However, none of these allowances are paid at a higher rate than the single age pension.
Refugees apply for social security through Centrelink like everyone else and are assessed for the different payment options in the same way as everyone else. The two-year waiting period for Centrelink eligibility that applies to other newly arrived permanent residents is waived for refugees and humanitarian entrants, in recognition of the fact that (unlike other migrants) they often arrive in Australia with few or no financial resources. However, Centrelink payments are calculated at exactly the same rate for both refugees and non-refugees and there are no separate Centrelink allowances that people can receive simply by virtue of being a refugee. (Parliament of Australia)