Yes, it is possible to undertake a HDR on a part-time basis for domestic or off-shore students. You are required to select that option in your application. As a part-time student you are expected to study for 18 - 20 hours per week (that is half of the full-time expectation). If you are also working full-time, you may be asked for confirmation from your employer that study release will be made available to you.
Keywords: Higher Degree by Research, HDR, part-time