I'm in the process of moving from an old laptop to a new one.
Am I able to just move my client copy of the svn repository from the old laptop to the new? Note that it has files in it that I'm not able to commit yet.
So effectively I want to move \\old-laptop\c$\myDev to become \\new-laptop\c$\myDev
Is this possible?
(I've searched for similar answers but I think they all refered to moving folders within a repository or moving the server repository.)
Yes, you can. Even if you are still afraid of losing something you can copy first, not move, and check if everything is in one piece.
Yes, that's perfectly fine. It might break if you install an older version of svn/Tortoise on the new computer than you were using on the old (an earlier minor version, i.e. 1.4.xx not 1.6.xx), but assuming you set up the new laptop with the latest Tortoise it'll all just work.
I'm not 100% sure if there are line ending problems moving your working-copies between Windows and Linux, though, but doesn't sound like you're doing that.
Alternatively, you could create a temporary branch and commit your work-in-progress to that? Then you'd be sure of not losing it.