Doing a full warm up concentrating on raising the heart rate, mobilizing the joints and activating the muscles and balance system is vital for injury prevention. Also for young goalkeepers doing a strong warm up concentration on proper movement mechanics can be a very valuable aspect of their holistic development as not just a soccer player but general understanding and knowledge of their body.
I also use this time for the goalkeepers to mentally prepare for the game ahead, teaching them to concentrate on the present and movements at hand rather than worrying about the game or thinking about anything non productive or of no connection to the game. It is almost like pre game meditation.
The video below is a warm up that I do with my goalkeepers before most training sessions and every game. I like to think of it as being specific to goalkeepers because the ball is in their hands, however, it can be done without the ball and useful for all players. I do not recommend going straight from this warm to a game for goalkeepers, you must them go through a confidence boosting handling and footwork warm up.