That's a bit smaller than the usual ones that are controlled by an Arduino
If the coil resistance is 230 ohms it would draw a max of 22 mA at 5volts so it could be driven direct from the Arduino I/O pins. What I don't know is whether it might produce back-emf spikes sufficent to damage an Arduino.
The code I linked to assumed that you would use a stepper driver such as a Pololu A4988 which would be like an elephant compared to your mouse.
Assuming there is no electrical problem the AccelStepper library should be able to control the motor.