Submit to a publisher directly. There is a dense concentration of publishers in New South Wales, including PressPress, Catchfire Press and Deadpan Press. Make sure that whatever publisher you decide to submit to allows for unsolicited submissions. If not, you may want to consider aligning yourself with a literary agent first.
Submit your work to a literary magazine. Some Australian publications you could submit to include Salt and Westerly. Westerly tends to publish works by new poets. Some literary mags also run periodic poetry contests, which is another great way to get noticed by other publishers.
Publish online. Some online journals you can submit to include the Cordite Poetry Review, Numbat and Malleable Jangle. You could also set up your own blog or Web site to share your poetry with the world.
Self-publish. Publishing a full-length poetry anthology can be expensive, but publishing a chapbook can be done quite cheaply. Many Web sites offer "on-demand" publishing, meaning you can print more books as you need them, often with no minimum order. You may also wish to check out SeaView Press, a self-publisher that caters to Australia and New Zealand.