I like to buy lovely locally-made handicrafts for friends and family who live overseas. Arts and crafts by Indigenous Australian artists are very beautiful, and while the big paintings by well-known artists are expensive, smaller items like hand-painted trinket boxes, carved wooden sculptures and baskets are a lot more affordable. By purchasing these, we're also helping to financially support artists living in remote outback communities. All major Australian cities have shops, including those attached to art galleries, that specialise in Indigenous art. When my family was travelling up in north-western WA a few years ago we saw a lot of gorgeous hand-carved boab nuts...you can't get more Australian than these! These can often be purchased on ebay. Just choose the 'art' tab and type in boab nut.
Art galleries in the capital cities and many museums also stock beautiful handicrafts by local artists, including drawings, sculpture, textile art, jewellery and much more. Wood carvings in beautiful Australian hardwoods are also a nice gift.