Welcome to iNaturalist!
Here’s the two options I can think of:
One, go to the Identify page and filter to see New Zealand or Australian observations. (I’ve chosen NZ in the link). Here you will see all the observations that need ID, and you have lots of additional filter options.
There are ways to see both NZ and Australia at once using advanced URLs.
Two, you can subscribe to a Place, or multiple places, in your case. Go to your Dashboard (home page) and find the Subscriptions box (should be on the right side). I’d suggest narrowing your subscription to a taxon you’re familiar with, such as Aves (birds) or Plants – you will then see all observations (including ones already Research Grade) in your All Updates / Following sections of the Dashboard. You also have the option to get daily emails notifying you of new observations in the categories you follow – under Account Settings.
Thank you for helping ID!