What state are you in ?
In NSW you simply have to store them so they are not accessible to unauthorised persons. ie lock them up.
You do not have to store them separately and the only restriction is you can only store 12kg of powder.
Legal to have unlimited ammunition, unlimited primers and up to 12kg of powder if you have a firearms license;
http://www.legislation.nsw.gov.au/#/view/regulation/2013/476/part3/div4/subdiv2/sec48Not required to comply with other storage if you hold a firearms license - paragraph (7);
http://www.legislation.nsw.gov.au/#/view/regulation/2013/476/part5/div4/sec84Unauthorised persons must not have access;
http://www.legislation.nsw.gov.au/#/view/regulation/2013/476/part5/div7/sec101ADI recommends that their powder is stored below 25 degrees C.
Some US powder manufacturers recommend that you store powder in a locked box made of 1 inch wood or other locked container that can blow out ie filing cabinet or thin sheet metal cupboard.
Note that smokeless gunpowder only explodes at very high temperatures but it does burn very quickly.
If it is stored in a strong container (ie a safe) burning powder can build up a lot of pressure until the container explodes.
Safes are NOT recommended for powder storage. Yes WA we are talking about you.
ADI says its powder should have a 10 year shelf life if stored under 25 degrees C.
I have heard from a few reliable sources that they have stored powder in a locked cupboard in their garage where the temp goes from 5 to 40 degrees for over 15 years and it still performed as expected. Not recommended but powder is reasonably robust.
For larger quantities most regs require separate storage for powder and primers.
I have a locked 3 drawer filing cabinet that I use. The top and middle drawers have polystyrene boxes (from diet meals!) with powder stored in them. The bottom drawer has primers. I have placed a 20mm plywood sheet in the bottom of the middle drawer (just in case).
I also lock the study door but this is more so I can leave powder in the press powder measure and still comply.