Can my autistic son be enrolled at a mainstream or special school on arrival?

Very difficult to gain any form of benefit for your child in Australia. Talk to WINZ.

Hi there - we're currently looking at moving. I contacted the Queensland Department of Education and asked this question directly - I would advise you to do the same so that you have in writing confirmation of their response.
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I was told Citizens of NZ whose principal place of residence is in Queensland, are eligible to enrol at state schools or non-state schools in Queensland.  
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For the school to receive financial assistance from the government for a student with ASD, the student must, in the first instance, have a formal diagnosis of the condition by a registered medical specialist (eg. Paediatrician, Psychiatrist or Neurologist). To receive assistance, the condition would need to be severe enough to result in activity limitations and participation restrictions for the student in the classroom.
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If it is not already done, the student will need to be verified under the Education Adjustment Program. This will detail adjustments that need to be made to the student’s educational program in order to assist them to participate effectively in the classroom. The school would normally organise the verification process.
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I really urge you to contact the Department of Education directly to ensure you have the correct information first hand.
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We also went and visited potential schools and spoke to staff - this really put our heart at peace that we were covering ourselves of any unexpected barriers to enrolment. Its soooo important especially with our kids on the Spectrum
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Blessings

sorry - in addition to my previous response, we are not expecting to qualify for any extra assistance like we receive here in NZ eg. CDA or Min of Ed assistance such as Speech Therapists, or hospital OT, Early Intervention Teacher - we are preparing to pay for these services ourselves.

me again ... we visited both mainstream and special schools, some mainstream schools were more prepared for ASD children, whilst others were open about them not having Special units and there would be limited support. We visited 2 ASD specific schools and 1 Special School, and a number of private Christian Colleges - the 2 ASD schools were private schools so there are fees that apply, the Special School is a Government school, so fees were not as high. All the schools were amazing - the Special School at this stage would be our choice to fit our current circumstances, whilst our other children would likely attend a different private school.