It depends on the budget, but if it seems that your dad is going to be spending the bulk of the money to buy you one, I would probably go with the Nissan or the Subaru.
Lexus is just a more premium version of Toyota. Since Lexus only has the RX series for a small SUV that comes in both petrol and petrol/hybrid versions. Toyota will not have any small SUVs, since you have the Prado, Landcruiser. The RAV4 is questionable, I've driven one and not really a fan of it, but that's just me.
Subaru with the Forrester but is more of a station wagon with large wheels instead of a SUV. You also have the newer Tribeca which is also good, but is expensive also.
Nissan has a lot of small suvs, the most popular being the X-Trail either in the petrol 2.5 litre 4 cylinder version or the 2.0 Litre diesel that comes from the VW Tiguan and Golf. The head room and visibility is very good; off road ability is ok; since it has adjustable 4x4 mode.
Nissan also has the Murano and the Dualis which are both good, but I prefer the Murano better.
Mitsubishi I'm not really a fan of any of their SUVs.
There is also Honda and Mazda which you have missed from your choice, as they are both Japanese car manufacturers too. Especially, the Honda CRV and the Mazda CX7 and CX9.
You should do a test drive if your dad is buying a brand new one for you, I believe the legal driving age is 17 for NSW and NT and every other state is 18.