Bind a key, and copy text from whatever your mouse is hovering over.
Chatframes, QuestText, Menus whatever.
You can bind a key from the blizzard key bindings configuration menu.
The following slash commands are supported:
/cpyt <Name of Frame>
This is mostly used for the chatframes, eg.
/cpyt ChatFrame1
you can bind keys to copy the frame that your mouse pointer is over, or the game tooltip (since you cant mouse over it).
I suppose you could also use: /cpyt GameToolTip