Anything that has had live things in it or been in soil or a tank situation would most likely have to be gassed to prevent any possible diseases or pests making the trip as well. I'm pretty sure they (customs) eradiate anything possibly contaminated with organics and its not a cheap thing to do and you would have to foot the bill.
If you have new supplies like filters. heaters, chillers, cooling fans or thermometers that are still boxed and have never been in your tanks they should pass through customs without an issue as long as the power points are the same as the type used over here.
If your going to be moving to around Brisbane area, there are lots of pet shops and fish shops that you will be able to more than likely get any sized tanks you want. Or you join various Facebook sites or Gumtree and find second hand tanks at times going relatively cheap. And for many other items eBay can be your best friend for hunting down hard to get supplies that local shops just will not stock. For shrimp I find any online fish shops put crazy prices on them, and no actual pictures of the exact shrimp you will be getting so its more a lucky dip or wait and see what arrives. So nearly all of my shrimp I buy from Facebook pages or word of mouth. That said however there is one online store I trust 100% for having great stock and incredibly helpful, which is Aquagreen in the Northern Territory. Aquagreen has lots of native and non-native aquatic plants, native fish (mostly endemic to the northern reaches of Australia and native NT shrimp. I have no luck with non-native caridina but my native caridina from the NT thrive and have never looked back since getting them a few years ago. They also sell fertilizers and some substrates and food. If you want a challenge (that being to stabalise and keep breeding true to a pattern) than I would suggest trying your hand at North Australian Chameleon Shrimp. http://www.aquagreen.com.au/plant_data/Caridina_sp_WA_4.html
Blackmore River shrimp are another sneaky change patterns and colour shrimp, just don't make the mistake I did in putting them with the Chameleons its near impossible to tell them apart now LOL. But they all get along fine together.
http://www.aquagreen.com.au/plant_data/Caridina_sp_NT2.html
You may have already searched such sites as this next link but in case you haven't have an explore of this, to help you decide if you want to import any tank goods.
http://agriculture.gov.au/import/goods/biological