Upvote:2
The minimum connection time for Delta Domestic to International at LAX is 45 minutes, unless your flight departs from the International Terminal, in which case it's 60 minutes - so either way you're officially covered.
If your outbound flight is actually on Delta then it should depart from Terminal 2/3. If it's a codeshare on Virgin Australia then it'll depart from the International Terminal.
Whilst this is technically a "legal" connection, it's one I would never take. The issue isn't so much that it's likely you'll mis-connect, but that the impact of a mis-connect is a 24 hour wait for the next flight to Sydney. Short connections like this are OK if there is another, later flight you can catch - but the impact of missing a 60 minute connection like this is too high for my liking.
If you do happen to mis-connect, then presuming both flights were purchased together the airline will re-book you on a the next available flight. Depending on the cause of the delay, they may or may not provide a hotel for the night.
If you can't book/change to an earlier flight for the initial flight it may be worth simply getting to the airport early and asking them to move you - although US airlines don't normally do this free of charge, in a situation like this it's certainly possible that they would.