The points cannot be transferred between the Wii & DSi.
Nintendo Points, formerly known as Wii Points, will not be as versatile as once thought. While the points are compatible with both the Wii and DSi, it is not possible to transfer points between the systems. For example a person registering a 3000 Nintendo Points card on their DSi will not have access to those points on their Wii.
Starting in November, Nintendo Points cards will be available at Japanese retailers in the amount of 1000, 3000, and 5000 points.