As far as general services for children and adults with special needs are concerned, Australia has nothing to envy to other countries: their level is top and especially for children with cerebral palsy there is a lot going on.
However it is important to be aware that some services (for instance staff helping at home and taking care of the child in order to let mummy have a bit of time off) are available to permanent residents only. And obtaining this kind of visa for children with special needs in Australia can be a rough and troubled path. Prepare yourself to a long wait and to several medical visits.
My daughter Benedetta obtained her visa (which is not a resident visa, but a 457 visa linked to my husband’s working visa) only for 2 years and after 4 to 5 months from our arrival, whereas the rest of the family got it faster and for a 4 years period (adults have to provide a medical check-up before arriving). Even the second and third renewal of Benedetta’s visa have been painstakingly slow, even if my husband enjoys the support of a solid enterprise that acts as a warrant for him and his family, and takes care of all the paperwork.
You might also want to enquire about leaving Australia when your visa has expired. I heard one case of a friend who was not allowed to get back in for three years. We chose not to go to Italy several times because of Benedetta’s visa that had expired and was taking a long time to be renewed (in this case you might want to enquire about the possibility to get a special temporary permit, we didn’t do it…).
All this happens because children with special needs potentially represent a cost for the government, that has to make sure your situation allows you to pay for any medical assistance your child might need. Last time Benedetta’s visa was renewed, my husband was asked to sign a document stating that should he decide in the future to apply for permanent residence, the government reserves the right to refuse it because of Benedetta. Moreover he had to engage to pay for any medical expense for the child. When all this has been done, the visa was renewed for 4 years.
All specialists like physiotherapist, logopedist, etc. for Benedetta, not to mention very expensive shots that she needs because of her condition, are paid privately by us.