Yes there is a Copper Rod Tool on the table of the enchanter's study.
Why could I not make the enchant when pressing the Enchant button?
It turns out enchanting is tricky. You need to click Enchant then click on some Enchanting Vellum items in your bags.
Form Blizzard :
"Enchanting isnt always the most intuitive of the professions and it can be confusing when you try to accomplish something in game but run into issues with nowhere to turn.
I was able to look into this, and it seems like the process works! You just need to remember to enchant some Enchanting Vellum when you want to make
To make the Gift of ... enchant, you need the Runed Copper Tool which I do not have because I am not an enchanter, and it's BoP if someone makes it for me, that won't work either. Please help.