Well, after being lurking peering the hits of three good sites, or at least reliable ones (grammarly, I mean) I would choose "My dream is TO...(activity etc. So - TO plus infinitive verb, then.)"
My dream is to go to Australia.
================ If you want to see for yourself. = = = = = = = >>
copy and paste into Google, or other search engine.
"my dream is" site:www.economist.com
"my dream is" site:www.theguardian.com
"my dream is" site:www.bbc.com/
There´s an interesting hit, if you ask me, here is it.
"My dream: to be able to drive a virus-powered car."
that is, used a colon to avoid the "is to be able", instead, he used just "to be able".
If you "personify" it (you somehow give live to your "dream"), then you could use
"My dream is going to Australia." (for example, if "your dream" is that girl that just boarded that plane, or is aboard the QE II and is just going to Australia).
My dream is going to Australia, and I won´t have another car like that Ferrari; ever. I reggret having sold her! " I dreamed of buying her so many times, and now this!