No. There are millions of firearms legally held by private citizens in Australia. For some reason, some gun rights groups overseas, especially in the US, like to claim we've been disarmed when we most certainly haven't been.
Having said that, there is certainly a higher level of gun control in Australia than in most of the US. All firearms owners have to be licenced. All firearms have to be registered. And the more 'dangerous' the weapon (the level of 'danger' being defined by law) the more complex it is to get a licence, and the more scope there is to refuse it. Just about anybody can get a basic licence to own basic rifles and shotguns as long as they don't have a recent (past ten years) criminal record, or a serious criminal record (longer term), but getting more than that takes some work.
But I've gone one of these:
and one of these:
Both held completely legally. The laws aren't good (and some are just stupid) - but they aren't as bad as they get painted.