Can I just go to Ireland and make the application there? Or can I make the application in London and then pick up the WHA in Dublin?

If you are an Australian or New Zealand citizen currently living in the UK or are passing through the UK en route to Ireland, you can lodge your WHA application with the Visa Office, Embassy of Ireland, London. If granted, this office will issue your WHA in advance of your travel to Ireland. It is not possible to collect your WHA after arriving in Ireland.