All major domestic and international carriers are served by Sydney Airports three terminals.
The International terminal (T1) provides the gateway to and from the rest of the world, with most of the best known airlines providing direct flights in and out of Sydney. Passengers using T1 will undergo immigration verification, in addition to standard security vetting.
There should be no need for concern, providing you have the relevant visa entry requirements. The immigration officers will be able to confirm this when running your passport through their computer systems.
T2 and T3 Qantas serve as the domestic terminals. Whether you are an international traveller or an Australian national it is important to know that a security check-up once you arrive at either terminal.