The two starting Isles for Draenei are loaded with copper. I quested there and raised my mining along the way until copper was grey. There's as much there as in the Dwarf starting area.
Either you don't have your "Find Ore" turned on or you haven't left a road. Heck, even then you can see quite a few copper nodes on the map. Make sure you have the ore tracking turned on.
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"the people can always be brought to the bidding of the leaders. That is easy. All you have to do is tell them they are being attacked and denounce the pacifists for lack of patriotism and exposing the country to danger. It works the same way in any country."
Hermann Goering, April 1946.