Hi
If You are thinking of something like mini helicopter following dog in a city or a forest while dog is roaming free, it might be very difficult to achieve, as heli would have to have 360° awareness of objects around it and follow clever algorithms to avoid them. If, however, You want dog to be followed in a football field or a park with no trees (or other objects in the way), depending on the accuracy required, You might get away with GPS chip only as a sensor and then microcontroller to gather and dispatch coordinates of the dog to the heli, and some means to transfer data (WiFi, 3G, 4G, RC, Bluetooth, etc.).