Is it OK to place ground plane under transformer?
It is generally recommended to keep all traces and planes out from under any inductive components. 
However, any well designed transformer will keep most of its flux contained.  After all, the point of a transformer is to transfer as much energy between the coils as possible. But there is always some leakage.
A copper ground plane can not provide any magnetic shielding - virtually none at all. [Note: This is only true at frequencies below about 1KHz; so does NOT apply to the the OP's application at 50KHz.] And there should not be significant electric field to worry about unless the the traces under the transformer are especially sensitive.
Power traces are generally very low impedance at 50khz so they should not pick up much voltage noise.
Keeping the power traces as narrow as possible and as close together as possible will minimize the magnetic effects.