In a nutshell, nothing happens without a rwc... Which can be issued by any govt. approved inspection station.
If the car you're buying is currently registered, you will need a rwc to change that registration into your name.
If its not registered, you will need to have the vehicle inspected, a rwc issued, and then you can register it.
Compulsory third party (CTP) insurance is included as part of the rego... And technically speaking that's all you need to drive the car on public roads, but you'd be stupid to just have that alone.
Third Party Property (shitbox insurance as we used to call it) covers the damage you do to someone else's car, but not your own.
Comprehensive is obviously full coverage.
If you buy a car in another state you have (I think) 3 months to obtain a rwc, cancel the out-of-state rego and then re-register the car in QLD.
You'll be needing a QLD licence or at least a CRN (customer reference number) before you can do ANYTHING with cars and paperwork though. Not hard to get one, you just gotta have enough ID, and something that proves your home address in QLD like a bank statement or power bill or something.