In short, Yes cover for the average Australian rock climber is available. There are many different styles and types of climbing and you can get travel insurance for some types of climbs but not others. View our guide on rock climbing and mountaineering cover.
Australian travel insurers do not provide cover for free climbing. However, it is possible to get travel insurance for rock climbing on graded routes.
Most travel insurance policies only cover basic trekking or hiking holidays, not mountaineering. Mountaineering generally requires you to use ropes, crampons and other specialised equipment, which will require specialised cover.