Auditory processing is assessed by an audiologist. Other professionals can do some screening, but in the end the audiologist is the only one who tests hearing. It is important to get a general hearing check done first, in case there are some conductive issues (which mean the hearing difficulties come and go, generally due to ear infections). Medicare will cover some of the cost of this assessment, but your not likely to get medicare to cover other services, unless there are other medical issues as well. The auditory processing assessment needs to be done by a educational audiologist, who is a specialist audiologist. They can do the original hearing assessment as well, just make sure it's the right person from the start.

The school may be able to advise of some local educational audiologists, and if they don't know they should have access to some allied health professionals who may be able to advise (a psychologist social worker, speech pathologist or occupational therapist or something, depending on your school and/or state).

Otherwise your GP will also be able to advise, and may check the ears as well and if required provide a referral for an ear, nose and throat specialist if it looks like grommets are on the agenda.