Which supermarket? Where’s Whole Foods? Etc.
There are also a number of 'convenience' stores, some of which - but not all - are co-located with fuel service stations.
Amongst them you'll find the 7-11 chain, as well as stores branded with the name of the fuel station. Most of these stores don't carry a full range of products, but will have enough items to get you out of trouble if you run out of the basics.
Which reminds me: What's the deal with Hungry Jacks???
I used to argue with our American friends who insisted it was Burger King! Well, it is but it isn't. The Aussie who started Hungry Jacks over here had lived in the US for a while, and saw an opportunity. But he also wanted to include to some Aussie touches. So we have better-than-Burger King 
Do drop in if you feel like food from home, and don't be surprised if there are some menu items you don't recognise - explore! Hungry Jacks has been in Australia for well over 30 years.
We have 3 major supermarket chains:
Coles, Woolworths/Safeway’s and IGA.
Coles and Woolies are the Big Two, locked in fierce competition; they also have associated petrol stations and liquor shops so hang on to your receipts for special discount offers.
(Note that Woolworths is not related to your Woolworths stores.)
IGA is a smaller independent franchise network.
You’ll find at least one of these three in any community, and now possibly an Aldi.
It’s best to check opening hours on the websites - we don’t do 24-hour shopping in most places, but you can order online with some and then pick up at an arranged time.
From what I gather, they’re a lot like your Trader Joe’s. Fresh deli items the assistants will measure out for you; fresh produce and flowers; fresh baked items (some bake on-site); fresh butchery as well as brought in; fresh seafood as well as frozen; etc. We have excellent food safety standards so you can feel safe about what you buy; you can return anything as long as you have the receipt. (The food was ‘off’, you felt sick, the product was faulty/didn’t fit etc)
Most will have an organic produce section, and in the fridges you can find plant ‘meats’ and ‘cheeses’. GF, diabetic and good vegan/vegetarian foods are usually in the ‘health foods’ aisle.
One of our most prominent health-food shop chains (Whole Foods) is Mrs Flannery - be prepared to pay a lot for shopping there. Some of the same items can be found in Coles/Woolies or an Asian grocery, if you have time.
Keep an eye out for the weekend Farmers Markets, and mid-week Sunset Markets - and for the fruit barrows in the capital cities! These really are a great heritage feature and the produce often comes direct from a local grower. Excellent value!