As long as the items are THOROUGHLY cleaned (recommend steam cleaning if possible) you are OK to bring it with you to Oz and I would recommend that you include them in your container with your furniture (if you bring in new or on the plane, you may be subject to duties). Remember to clean children’s toys as well.  Do your research for the cost of moving and you should be able to get competitive quotes on this.

You can bring any wine, spirits etc into Australia (and you should bring your wine collection!). Make sure it is in your container, and you will pay duties on these items. With wines – list all the bottles, include vintage, brand, and approx. value of the wine (what you paid for it) – makes calculating the duties easier.

If you have a really state of the art mobile (cell phone) – bring it over and just get a new sim card here. In most cases however, you get a phone here free with any contract.

If you have a PC or fax or any office tools you want to bring over – do so (and bring them with your container – not separately.  But do not go and buy these items to bring them over – they are generally very competitively priced in Australia.
As a rule, it is simply not worth bringing your vehicles (of any nature) to Australia – the import duties and taxes are very expensive.
Vehicles must generally comply with Australian standards before customs will release them – and this too could end up costing a small fortune.

As for actual furniture, generally good quality furniture is expensive in Australia – including good quality bedding etc – you do get very cheap and reasonably priced items as well at several stores, but it is still worth the cost of bringing over as much of your furniture and goods as you can.  And finally with your electrical appliances, you will most likely need to replace the plugs on them. Decide if it is worth the hassle and cost to do this.