Would anyone know the translation of the following state names in Irish:

Victoria
Queensland
New South Wales
Tasmania

For the most part, place names outside Europe are not "translated" (though there are some exceptions). Instead, they are transliterated, which usually means rendering them in a phonetic way which uses Irish orthography.

Some foreign place names have special forms in Irish, usually because the Irish were in contact with them back when most people spoke Irish as their everyday language. So, for example, Norway is An Iorua.

Sometimes, as with Norway, the have an added definite article ("the"). That also happens with Australia itself: An Astráil, and also Tasmania: An Tasmáin.

The letter "v" is used in Irish only in words of foreign origin, and often stays unchanged, and Victoria follows that pattern, remaining as Victoria.

Although there were Irish-speakers in New South Wales early on, that state name also remains unchanged, as does Queensland. South Australia and West Australia are actually translated, however, as Deisceart na hAstráile and An Astráil Iartharach, respectively.
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I'm not a native (or entirely fluent) speaker, so be sure to wait for confirmations/corrections, especially for tattoos.