Hi Melissa,
Have a look at Trinity Anglican School - there is one on the southside of Cairns, and one on the northern near the beaches. TAS has a very good reputation. We are looking at sending my boy there when he's old enough... The southside of Cairns, is alot cheaper than the northern beaches...there has been alot of new residental development, and therefore, it's quite cheap at present. Mt Sheridan/Forest Gardens is only about 10 minutes from Cairns city via the "back road" and almost accross the road from TAS school. Edmonton is slightly cheaper again, and about another 5-10 minutes south from Mt Sheridan, depending on where abouts in Edmonton.
Edge Hill/Whitfield is a very prominent area with a Edge Hill Primary School. It has a fantastic reputation, and great for primaray school. It can be expensive here, as it's 5 minutes to the airport, botanical gardens, and the city.
The beaches are also great to live - more expensive than the southside. New developments like Smithfield Village seem reasonable. Clifton Beach & Palm Cove beaches are lovely places to live if you want to be near the beach, but can be very expensive.
I grew up in Cairns, and went to Edge Hill State School, and Smithfield High - they were both great. But if you are looking at private, TAS would be worth a look.
All the best. Let me know if i can help with anything else.