Unfortunately there are two problems here. First, to search for records in Ireland you need to know where the family lived (parish if not actual townland not the name of the county or just 'Ireland')- although a fairly uncommon surname like Smithers might help. Second, civil registration for births (and deaths and Catholic marriages) started in 1864 so you need to search for church records, etc. which means you have to know where they lived.
Australian certificates are so much better than Irish ones- any more clues from death certificates, etc.