Can I look for a new post-doc without informing my current PI? I'm thinking about leaving my current lab, since it's moving to a field that I'm not really interested in.
I am thinking of contacting other PIs that work on topics that are a closer match to my research interests, to see if they are interested in starting a project together. 

I am concerned that if I talk to my current PI before taking any steps, she could bad mouth me to prolong my staying in the lab, and to prevent leakage of the lab's knowledge. So from this point of view it would be my best interest to inform her as a fait accompli when I find a new lab (while still giving proper notice).

I still have some reservations about doing things behind her back though. I would like to leave on good terms, and since academia is such a small community doing this could affect my reputation.
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"?)