Switch on/off MP3 player by using transistor

Have you tried 100 ohm base resistor?

A BJT as a switch needs about 10% of the load current supplied to the base to saturate properly.

Your MOSFET isn't logic-level unfortunately, and some logic level MOSFETs are only good for 5V anyway.

ZTX851 is the best BJT I know for switching.

You don't have a 2N2222A ? That's the common switching transistor - only good for say 0.6A when
driven from an Arduino pin due to the need for 5 to 10% base current of course.

logic-level MOSFETs are the thing to use for higher currents.