Hi yes VCDS or OBD Eleven will do the job, the OBD is the cheaper option and just as effective it should identify the rogue injector and allow you to code the new injector, if you don't code the injector it will run rough, the superior scanner will also allow you to re adapt sensors and batteries as well as release the parking brake should you wish to change the pads, [brake service position] it will tell you which speed sensor is playing about, the list is endless, I can recommend OBD ELEVEN PRO as it covers multiple VINS on every vehicle in the VAG range, is all you need is a reasonably new Android phone and away you go. Welcome to the world of modern cars!
Steve.