I think you are confusing a few different technologies.
GPS only receives signals from the GPS satellites, for this it just needs an external antennae. It isn't going to work with an implanted device in a dog.
Radio directional finding (RDF) transmitters used to track migrating animals broadcast a continuous signal which is followed by simply looking for the direction that the signal is strongest and assuming the animal is in that direction. Again you need an external antenna and more power than GPS (modern tag systems actually find the animals position by GPS and broadcast it by cell phone)
RFID comes in two types, powered and unpowered. If the tag has power it can broadcast a stronger signal or use a smaller antennae and work over 10s of meters. An unpowered RFID tag - like the tags used to 'chip' pets uses power broadcast from the reader and only work over a few cm.