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MS Web Designer Team
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Dallas here from the Social Care team at Shopify.
Since you are wanting to make custom items rather than dropshipping you will want to use what is called a Print on Demand service. POD is like dropshipping (where you are able to sell products to your customers, but you don't have to hold on to any inventory at your location. When an order gets placed with you-you would then order the products from the suppliers. Your suppliers would then ship the products out to your customers for you), however, rather than just choosing from a catalog of items you can actually design your own products. If that is what you are wanting to do then I suggest services like Printify or Printful. Now, they aren't located in Australia, but they do ship to Australia.
Printful is my favorite, in personal opinion, just because you do have the ability to purchase your own products, send it to them and have them ship it out in the same way as with dropshipping.
As far as actual Australian dropshippers are concerned you would want to look at
These will allow you to make custom t-shirts to sell to your customers. If you want to add bags, mugs, hats, etc. You will want to look into the first two that I suggested.
Now, you were saying dropshipping and not POD so if dropshipping was in fact what you were wanting to do then you can choose from options like:
These options won't allow for custom made items, as I said before, but there may be some things that you are interested in adding to your store. If you would like some more information on How Dropshipping Works this link here will take you to a really handy document. Another great resourse is the Ultimate Guide to Dropshipping.
I hope these options help you with what you are looking to do, but if not then please let me know. I will be more than happy to help you in any way that I can.