I am an Australian permanent resident (however not a citizen) and plan to travel to Italy with my Austrlaian husband and Child for one week holiday.
I am a Thai National living with a permanent status in Australia married to an Australian Citizen.
Your permanent residency means nothing when entering a 3rd country, to them you are a Thai citizen. You will need to apply for a Schengen Area tourist visa (Italy is in the Schengen area of Europe) via the Italian consulate in your city.
Make sure you can re-enter Australia too, check out this page: http://www.immi.gov.au/FAQs/Pages/i-am-a-permanent-resident-what-documents-do-i-need-to-come-back-into-australia.aspx
I'm assuming your child has an Aussie passport - otherwise you'll need a visa for them too.
Don't forget to get travel insurance too. www.worldnomads.com about 5 years ago