A co-worker tells you in confidence that she plans to call in sick while actually taking a week's vacation. What would you do and why?

Firstly she shouldn't put you in that situation if she is your friend, very awkward as it was said in confidence! Personally I would tell her that I would have to say something if I thought there was going to be any adverse effect on the company or her colleagues.

First I would like and do my best to convinc her that she must not do it, she must not lie to the company she is working for.

If she still insists, I will be a whistle blower.

I am agree with  Peter Scott answer.