I'm pretty sure everything you need is contained in the repo folder. (The .git folder under there contains all your history/changes)
So you should be able to simply copy the entire repo folder to D: drive in window explorer.
I can't remember if there any any hidden files as part of a repo folder, but you might want to check that or enable "show hidden and system files" in windows explorer just to be safe.
Once you have a copy of the repo folder on D: you should be able to add that one too sourcetree as a new repo, if you want.
(file open, select the folder). It should find all the history inside the .git folder and just make a new TAB in source tree. Though you might want to rename the folder so you can tell them apart.
However without an online copy to push and then pull from it's hard to sync the two copies.
I guess you could simply schedule an automatically xcopy/rsync in windows to copy the folder to D: every time you start up the PC.
An online git copy is easier and would give you a backup which is I'm guessing why you are trying to make a D: copy.
Setting up free Atlassian git account is pretty easy, if putting your source online makes you feel uncomfortable a lot of big companies use it for storing their source. Just make sure you setup the Atlassian repo as a 'PRIVATE' one