"I am going to go to Australia next year."
I believe the English sentence should be "I plan on going to Australia next year" so that it requires つもり. As it stands, the sentence seems a bit ambiguous as 来年オーストラリアに行くis also a valid translation of the first sentence.
This is wront as the つもり indictaes intent. The sentence clearly states they are going to Australia, as if their ticket is already reserved.
I wouldn't say it's wrong. If I plan on going swimming next week I would say " I'm going swimming next week", rather than " I plan on going swimming next week". Your translation is more literal and should be accepted, but it's not necessarily more correct in it's spirit. Persosonally I'm not a fan of literal translations since it only makes people try to translate everything literally while speaking Japanese leading to weird non-understandable sentences. It's better with variations, making the students think about different meanings of the same sentences.
It should be either "I plan on going to Australia next year" or "I intend to go to Australia next year".
The words "plan" and "intend" show intent. The purpose of つもり is to show intent. つもり is not 絶対に or 必ず. Therefore I believe the above changes should be made.