It is actually very common in federal systems to have state/province-level taxation, driver's licensing, etc. I don't think the US is particularly peculiar here at all. Canadian provinces also have individual GST and income tax rates.
In some ways, I'd say Australia is actually more peculiar than the US, in that the Australian states have significantly more limited taxation powers than American states or Canadian provinces do – here, the federal government banned state income tax and state sales taxes (GST/VAT), forcing uniform national tax rates and collection for both. However, Australian states still retain the power to levy some other taxes independently, such as land taxes and payroll taxes.
In some ways, I'd say Australia is actually more peculiar than the US, in that the Australian states have significantly more limited taxation powers than American states or Canadian provinces do – here, the federal government banned state income tax and state sales taxes (GST/VAT), forcing uniform national tax rates and collection for both. However, Australian states still retain the power to levy some other taxes independently, such as land taxes and payroll taxes.