Ok, so this "new guy" wants you to work a couple of weeks, you say. What exactly does that mean? You'd only work there for two weeks? I'm confused on that part.
About giving notice to your current job. It doesn't matter if she is there or not. You can put in your two week notice now. That would still be one week after she gets back and it gives you time to get the loose ends tied before you leave.
While I'm on my own quest for a new job, I always keep one thing in mind. I come first. I must do what is right for me and only me. I have been feeling guilty about leaving my job, but I can't do that. They will find someone else to do my job, I know that. That is always something to remember.
So, I wish you the best of luck with whatever you decide. Sorry I was not much of a help.