I know, but I don´t need that tiny amount of current. 200mA or more would be fine.
In addition I have to charge it with an "air-distance" of ~4cm between primary and secondary coil.
I suspect that needing/wanting a 200ma charge rate and 4cm of distance between the coils using air as the magnetic coupling media is going to take very large coils and probably not practical. There is a reason most power transformers of nearly any wattage use a ferrous metal as the magnetic coupling media. Air is pretty inefficient for transferring power.