Abruzzi17 wrote:what does that have to do with anything? the only 2 countries which recognized dual citizenship are Italy and Ireland. Not Australia.
Not true. In fact, there are many countries that recognize dual citizenship, including the US since 1992 (which is how most of us have US/Italy dual citizenship) and Australia (leading to Australia/Italy dual citizenship).
In terms of obtaining citizenship jure sanguinis, there are again many countries that also have this policy, including Italy, Germany, and Ireland in the EU.
As for the OP - if you're just traveling, why do you need a second passport? An Australian passport will get you up to 90 days in Italy. I do not have direct knowledge of how the process works in Australia, but in the US, obtaining an Italian passport costs US$1000+ and usually takes several (2-4) years. If you are just planning to travel for a few weeks, it makes sense to just go on your Aussie Passport.
If you still want to proceed, what we need are dates of birth, marriage, immigration, and naturalization.
Who was born in Italy? Your maternal grandmother? When was she born, when did she immigrate, when did she get married, and when (if ever) did she naturalize? Where and when was your maternal grandfather born?
You're going to have to figure out some family history before anyone can tell you if you qualify.
