Likewise in Australia. The only difficulty I've found using a debit card in recent years is when renting a car: with a debit card, they generally want to put a "hold" on the account for a few hundred dollars.

I can't get a credit card anyway since my income isn't high enough, and I wouldn't want one because they charge annual fees in Australia.

Banks in Australia run their own payments system, so it's possible to pay by card without going through Visa / Mastercard. Some cards issued by banks don't even have the Visa / Mastercard affiliation, but I think the Visa / Mastercard debit feature is needed it you want to make card-not-present transactions online.