Taxation of foreign pensions

I am thinking of moving to ROI as I have an ROI passport although I am from Australia.  I receive an age pension from Australia and need to know if I will pay tax on it in Ireland.  My pension is not taxed in Australia as it is a social security pension.  I have read that such pensions are NOT taxed in Ireland if they were not taxed in the country of origin, Australia.  I have also read that I do not pay USC on foreign pensions.  Is that correct?

All advice gratefully received.  Thank you.