Do you have to go to the Mainland to buy groceries and other essentials in bulk?

Also Woolies deliver to the islands, each week, maybe as much as 3 days a week dependent on which island you live on. I think any order over $300 is free delivery with Woolies, with a sliding scale increasing as you buy less. I think $15 is the dearest you will pay for delivery with them. You can get a frequent delivery card with Woolies, for $99 and that will cover you for all deliveries for 12 months, I believe.
No Coles deliveries here

There is a super IGA store on the island with prices pretty much the same as Australia that have everything you would need as well as a butcher, newsagency, pharmacy, and most everything else you would need as there is a large amount of retired people living here, rent for a 1-2 bed house is around the $180/week mark and maybe a little more if you want it within walking distance to the shops and ferry.

Woolies deliveries on all islands I believe (not 100% sure whether Karragarra gets deliveries, probably do), approx 3 days a week now (at least on Lamb Island) since COVID appeared, as the authorities were worried they would have a real problem on their hands, where people would have no food or ability to buy enough when lock down was on, so they negotiated wit Woolies and extra days have been put in place, so that is one good thing which came out of COVID as people had been asking for more deliveries for years. You can purchase a yearly delivery deal through Woolies for around $110 (?) where you can get as many deliveries as you want. Also IGA on Russell, Spar and 5 Star on Macleay, no supermarket on Lamb, only a corner store and no store at all on Karra