Does a gold detector exist?
You ask:


  Does a gold detector exist?


Absolutely. Here's a metal detector that is fine-tuned for gold detection, available ${\it via}$ Amazon. 

That said, if you are looking for something that detects only gold, I'm not sure the best way to proceed in that case. This site appears to be a comprehensive review of some popular precious metal-tuned detectors on the market. The site is maintained by a person with an active interest in prospecting and metal detection. It is stated on the linked page that:


  A quick note to those who know nothing about these machines. These are metal detectors. There is no such thing as a "gold only" detector. These detectors will also find lead, copper, aluminum, and other metals. These units are best used to look for relatively larger pieces of gold at relatively shallow depths. Concentrations of gold dust are not detectable. Some of these units can hit gold that weighs as little as a grain (480 grains per ounce) or less but only at an inch or two. Only the larger nuggets can be found at depths exceeding a foot. Only world class nuggets weighing many ounces can be detected at over two feet. The vast majority of nuggets found are found at inches, not feet.


In any event, you can purchase a device which has been engineered to discriminate base metals from precious ones (such as the model I have linked here).


  Also, does a metal detector detect gold?


Yes - see the reviews for the product offered at Amazon (and many others like it) as well as the informational site I've linked (above). Also see the Wikipedia page on metal detectors for more information, including the issues relating to fine-tuning the devices to discriminate between metals with similar/different properties "detected" by the devices.