In Australia, there are 2-3 major hardware stores (Bunnings, Masters, Mitre 10), all of which sell pretty much the same Pine wood/MDF/particle board from the same suppliers. 

I'd like to work with wood that isn't Pine/MDF/etc but I realized I have no idea where I could buy it from aside from those three places.

Is there a specific type of store that sells wood? A timber store (I don't even know if that's a thing!)? I'm after high quality hardwood and I don't want to buy online as I expect the shipping would be very expensive for large quantities.