Quitting a job?

I am currently a nanny/sitter, but got a new job as a preschool teacher. The new job pays alot better, and is only blocks from my house. The problem is, I have to have alot of shots and tests before I can start, but couldn't get a dr's appointment until the Friday before I start the new job on Monday. My question is: How do I give or not give a 2 week notice to my current employer? My fear is I will put in my notice, then some test will go wrong (not sure what, there are TB tests, chicken pox tests, etc.), and I'll have already put in my notice and will be left with no job at all. How should I deal with this? I don't really feel bad about not giving her a 2 week notice as she really takes advantage of me and treats me rudely, but I feel like a notice is only fair. On the other hand, I need to look out for myself forst. I can't be without a job. What to do???/