Can I look for a new post-doc without informing my current PI?
In my experience, people who have been in a field a long time all know each other, even if only peripherally. If you do apply to another position, there is a real possibility that the the new PI will simply call up your current PI and ask about your qualifications etc.  

To me, it seems completely reasonable to tell your PI exactly what you say in your first sentence. You could even ask for her help -- if you are this uninterested in your current position I doubt she will go out of her way to try to retain you. (Also, if you are indeed looking to move to a lab that does not compete with the current one, can she legitimately be concerned about intellectual property "leakage"?)