Bushwalk Australia

Hello,
I'm currently doing a exchange and living in Brisbane and I have a free week in june that I'm planning to use to explore around. I had a look online and found out about these great walks and that caught my attention so I came up with a list of what I'd like to do while I'm here in Australia. So far I got Fraser Island Great Walk, Thorsborne Trail and Carnarvon Great Walk on my list, it might be a bit optimistic give the limited time I have here but it's good to have options.
I was thinking about doing one of these great walks in the second week of June. For what I read online the only way to get to Carnarvon Gorge is by car, is that it?
I don't have a car so my plan was to use public transportation or to rent one to get to the places. The problem of renting a car is that the car would be sitting in the park and I would be wasting money while i do the track. Now it seems that the Fraser Island Great Walk might be my best option. Do we have to walk a lot on sand? How hard is it?

Do you guys have any other suggestion on multi day tacks around this region?

Ok try Lamington NP. You'll have to drive to either Binna Burra side or Green mountains ( O'reillies) . You can base camp at Green Mts and do day walks or over night walks or do the 42 km Binna Burra to Green Mtns and return .
You could go do the great walk in the Sunshine Coast hinterland . It has several stages and can take 4-5 days.
I'd also recommend catching the moreton island barge over to moreton island and walk south and cam day 1 on the western beach camp ground , then day2-3 on the Eastern side camp ground and base camp there doing the large sand dunes to the south and back.
There are heaps of options. feel free to pm me if need more ideas as I'm from up this way . If you are here for a while. Consider joining a bushwalking club. Heaps here and I can recommend a few if needed.