Visa for you and your partner are not usually difficult, non O is best and cheapest option, your doctor does not need blood test to sign medical report.You must be in Australia when you apply.
I am not sure if you and you little dog are all still in Australia, but if so, I think the your dog will be your biggest cost and administrative issue.
The cost of transporting a dog out is if you fly him/her cargo, but does require alot of paperwork and time ( and rabies vaccine).
The big expense will be returning your dog back to Australia. Return transport plus compulsory quaranteine in Melbourne ( the only facility in Australia), usually well over $
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aus.
We are retired, and have our beautiful dog with us, but do not intend to return home permanently until he passes.