I am traveling to Australia first time. My departure date is stamp on my passport from my country. I landed on Perth and gone through all the immigration process than I fly to Sydney through domestic airlines .After few minutes I show my passport and didn't find the immigration/arrival date stamp on my passport. So I am worried if this gonna put me on trouble.
You should be fine. Australian immigration records and visas are all electronic, so arrival stamps are not required and officers typically don't even bother looking for them. (This also translates to an irritating habit of stamping in and out on random pages in random order, but I digress.). An increasing number of nationalities can now use fully automated entry gates, which do not stamp.
That said, it is slightly weird that you were not stamped in if you arrived on a tourist visa and were inspected by a human. You've done nothing wrong, but if you want to be extra careful, hold on to your boarding card for the flight to Perth and bring it with you when you leave.