The transistor you don't know what is for is limiting the current, for protection.
The major issue I see with this is the very very low efficency and high power dissipation, as your input is 11V you need to dissipate almost half the power, or almost the same going to the load, that's 36W!! you will need quite a chunk of aluminum and a fan to do that!
Do you need to be efficient? Can you have such heatsink?
Is your input voltage fixed? Still with this design you will need at least 8V and still dissipating 12W, different topologies could do better, using maybe 7V input and be fine, just dissipating 6W. If not you should consider a SMPS. Still low voltage high current supplies aren't very efficient by nature.
JS