The part to convert video over cat 5/6 is called a balun.
Why do you want an IP cam for a baby monitor? Wouldn't it be easier to use an analog camera that can be viewed on a tv rather than having to pull it up on a computer's monitor?
*edit*, sorry, just saw the part about allowing grandparents to view the baby at night. Still think a simple ir cam would work better and be more cost effective.