I think you'll find copying the hyper-V data files will be a little bigger than you expect, "I could easily move from my desktop to my laptop" .. after copying a 20 Gig hyper-V drive, yes.. first think how long will that copy take.
What you really need is to install the dev tools on both machines (a 1-time cost) and then work on your code using a source control system as if you were 2 people accessing the same repo. When you want to use the laptop, you (ensure you have checked in all the code) check it out on the laptop and work away. When you're ready to move back - commit and checkout on the desktop. You have the benefit of source control too then, and a faster development environment.
You can run the SCM server on the desktop machine and still checkin/out on the desktop too, but then you'll only be able to commit when plugged into the same LAN. An alternative would be to get a "cloud" based repository to commit to.