If you have the budget a company called Axis
makes some IP cameras that are really good. Or, also with a sufficient budget, you can create your own DVR (digital video recorder) with a Synology NAS and their surveillance station
If you are looking for a solution with an existing laptop you can try:
(claims to be open source but removes all comments from open source code, Windows)
However, your requirement was to run undetected. If this is a computer that the "nanny" will be using it will be a bit more difficult. If you are using iSpy you could always log in as your own user, run it, switch users, and then let the nanny have her own account. They would never see it running.
If you want to be even more sneaky you could run the ZoneMinder VMware Virtual Appliance using VMware workstation in the background but that is a more advanced option that requires a bit of finesse.
If the nanny isn't computer savvy you can try WebCamImageSave
but it will be easier to detect. I have not used this software though and cannot attest to its effectiveness or quality.