Giving notice. Weeks required

Just found out my wife is being transferred so I'll be giving my notice at work. I know legally I'm probably not required to give any notice but I understand 2 weeks is a professional courtesy. I've only been at the place since February and wonder if 1 week is enough. I think in my contract it states after 3 months if I give notice they can shorten it and I'm only elegible to receive a weeks pay anyways.

Any thoughts?