Upvote:4
Assuming you are an Australian citizen, or a national of another country with visa-free privileges in the Schengen Area, or otherwise have a visa valid for Schengen, you may enter within the short-stay rules.
Your days spent under a residence permit in the issuing country (theoretically; practically there are few ways to check) do not count against your short-stay limits; you should be prepared to demonstrate this using your expired residence permit or another official confirmation of your residence. Although Australian citizens do not usually face much scrutiny at the border at entry, exit immigration checks are relatively common to ensure you have not overstayed; but this should be straightforward, especially if you are exiting through Denmark (the country that issued your residence permit).