Sure it is possible but fitting a 2.0 16v turbo is a *lot* of work. Ever looked in the engine compartment of a Q4? Little crouded aint it?
Unless you have a lot of time on your hands, a place to work in forever and the skills of a good mechanic i wouldn't even start.
Almost forgot, you also need the money to back things up!
Much cheaper to buy a Q4 and get some extra parts to make it all like new.
(A turbo engine also has an oil cooler, a turbo, an intercooler, different ecu, different clutch, bigger brakes, stronger gear box and the list goes on!)