Batman needs his Batarang. If I had to name two tools that every incarnation of Batman has, I would pick his Batbelt and his batarang (this UGO article agrees, too).
So I've started shopping for a boomerang. I couldn't find a local shop which kept them in stock but there are plenty of good places on the web to buy them. As always I know nothing about this Batman skill so where's the best place to start looking? Wikipedia. From there, I happened to find Canboom which made me realize that most countries probably have a national association so of course Australia does, America does and many more.
I recommend looking at
But in all honesty how good of a weapon is a boomerang? They are really light and there's very little information about them being used as a weapons (perhaps even some dispute) but it sounds like you can throw them super fast and the edges could be sharp-ish so maybe... According to this site much heavier throwing sticks would have done most of the killing while boomerangs would have been either for communiction or distraction. For a really brief history of boomerangs checkout the REDI or Boomerang Association of Australia websites.
I'd be willing to bet that a real-live Batman would use BatShuriken not Batarangs. In fact, many comics show Batman throwing sharp objects that don't return and this is definitely what the modern family of movies shows. Shuriken are considered non-lethal weapons that are used mainly for distraction purposes. They would be perfect for Batman...
But the Batarang is definitely more canonical or mainstream or classic and so we'll learn to use it first.