Make a copy of your current character’s folder in the /wtf/ folder. Copy only the “SavedVariables” folder if you want just addon settings, or copy the rest for bindings etc. Most addons will keep the settings across servers (I think) Character specific settings for non-profile addons are in World of Warcraft\\WTF\\Account\\ \\ \\.
Where to copy addon settings in World of Warcraft? The easiest way for all other addons is to go into your WoW -> Interface -> WTF -> Account Name -> Server -> Character (that you want to copy FROM), and copy everything in that folder over to the folder for the alt you want to play, and replace everything. How to transfer character and add on settings in Wow?