Will this power supply work for my stepper motor?

I am still very new to electronics. I would like to move a stepper motor with an arduino and the motor shield.

The motor:
http://www.mitsumi.co.jp/latest/Catalog/compo/motor/m42sp13nk_e.html

The Shield:

The power supply is a Power Wheels charging cord that I found at a flea market. The back reads Output: 12VDC 1.2A.

Can I simply cut off the adapter, strip the wires, and attach them accordingly onto the shield without damaging any of the components? If this power supply will not work, can someone explain why? I appreciate any help!

That motor is rated for a current-limited PWM bipolar driver, its winding resistance is 4.2 ohms (at 12V that would pull about 3A, the maximum winding current is 0.6A). Standard motor shield is not the the right way to drive it.

[edit: I think "chopper driver" is what I really mean. something like the Polulu A4988 driver...]