Many knives are banned in Australia yes. I don't know off the top of my head which ones specifically, if it could be controversial to anyone, it's banned. But that's just ownership, possession of any knife in a public area without a "genuine occupational reason" is prohibited no matter the kind. Except a Swiss army knife or similar, or a knife used only to cut food in a picnic or something.
Pepper spray/OC spray/mace is also banned, as are stun guns and tasers, airsoft guns, handcuffs and even body armor (can't be permitted to stop police shooting you after all). In fact all of those could be said to be MORE illegal than guns and knives, some guns can still be obtained so long as you have a "genuine reason" (of which self defense is not one), fill out piles of forms, undertake a couple day course, join the aussie equivalent of the NRA depending on your genuine reason, buy a safe and mount it to the floor of your home and submit to random inspections of said safe (the cops come to your property and ask to be shown your storage setup), get given a background check, provide references and fork over some cash.
In fact, under the law, if something looks convincingly like a weapon of a restricted category of firearm, it is considered by law to BE one of those categories of weapons. So a lot of replica's and similar things are illegal too.
Crossbows, and bb guns are also restricted requiring the same process as for guns in theory, in practice the law requires the establishment of some governing association along with local clubs which none of those things have much of in place. So they're more or less out too.
Laser pointers are the newest edition in the same category as knives, can be owned but must not be carried in public without a genuine reason. No stores sell laser pointers anymore, you have to buy a much more expensive "presentation pointer", which is basically a device with sensors that transmits to your computer allowing you to move the mouse as if it were the dot of a pointer. If it's a laser pointer over 1mw it requires a permit of some kind and membership in an astronomical organization to own.
Technically it is indeed a state by state thing, but in practice it's not. Prime minister John Howard, whom introduced most aspects of these laws in question forced the states into complying by threatening to withhold tax revenue from the federal government. Much like the highway tax trick in the US. except unlike the US. State by state law has never been all that different in the first place. There are still some minor differences, in regard to weapons, roads and other state matters, but increasingly more gets synchronized to the federal governments wishes. Also there's only 6 states to get on board. So each state is extremely similar compared to the diversity of American states.
Most Australians I know would rather abolish states entirely and put all their authority in federal hands.
EDIT: funny little side note, I was having a conversation the other day about the problem of domestic violence and family violence against women and children the other day since its been in the aussie news lately. And I had a semi-joking idea. All these mass shooters, most of these perpetrators of shootings and domestic violence. They're nearly all men... hypothetically what if we made it so guns were banned, but only for men, and women could buy and carry a gun should she want too. I'd be curious how that'd turn out. I mean if anyone should be allowed to have a gun, surely it's a woman. We barely murder or rape or slaughter anyone. 
