Here's one that's been around for a while and had slipped my market-listing net:
Southerly is one of Australia’s oldest continuous literary journals. The journal of the English Association, Sydney, it was launched in 1939 with works by authors such as AD Hope and Kylie Tennant. It was, from the outset, dedicated to publishing new Australian literature of the highest standard, and of providing a link between the academy and the garret. Southerly continues to publish the best in new fiction and poetry, reviews and criticism, from and about Australian and New Zealand authors. Southerly is published three times a year, both in print and digitally, and is complemented by a free online section, the Long Paddock. Our entire backlist is available online through the Informit Literature and Culture Collection. Our blog provides commentary and bibliophilic musings from a different writer each month. We are open for submissions all year round.
They're after short stories and creative non fiction from 2,000 to 8,000 words, as well as poetry. As tends to be the norm for literary markets, there's no payment listed, but I'm pretty sure there's payment.
Full submission guidelines: http://southerlyjournal.com.au/submissions/
And Literarium market listing: https://literarium.net/market/brandl-and-schlesinger/southerly-journal