If you find a baby possum, it may be very cold, sick or injured. The fact you could pick it up often means there is something seriously wrong which prevented the animal from hiding or running away. Without experience it is very hard to assess if the animal is injured because it knows not to exhibit pain or disability since that behaviour attracts predators.
Can you rear a baby possum?
It is likely that a baby possum you have found has fallen off its mother, probably because she has had a collision with a car or been attacked by a cat or dog. Vehicle collisions and animal attacks often cause internal injuries that you cannot see. If you take it home, it may well die a painful death several days later from a problem that you cannot identify.
So the best action is to take it to a local vet who will examine it for injury and then pass it on to the RSPCA or a carer who has the knowledge of the animal’s needs and special nutritional food supplements. Even experienced wildlife carers find a high percentage of baby possums that come “into care” will not thrive. Perhaps their mothers knew they had a health problem and it was not just bad luck that they lost their mother.
If you would like to care for native animals, there are several excellent organisations that provide training in Brisbane (Google organisations called Wildcare, ONARR and BARN). You can then try rearing with the support of more experienced carers and access to vets who will often provide help at no charge.
After training, you are permitted to look after certain native animals for short term care only until they can be released again, under a special licence issued to the organisation, which will expect you to continue with extra training to improve your knowledge.
In summary it is not permitted for you to have an injured or orphaned native animal at home without a Wildlife Rehabilitation Licence. The reason is simply that it is difficult to be sure the animal is healthy unless you have training and support from others with experience. So finding and keeping a native animal, even if you think that is the best outcome for it, is breaking our wildlife laws and probably not in the best interests of the animal.