Can I remove my hdd from my mid 2010 MBP and put it in my girlfriends 2012 MBP and it just "work?"

Can I remove my hdd from my mid 2010 MBP and put it in my girlfriends 2012 MBP and it just "work?" I have a few reasons for wanting to do this, but one reason is BootCamp/Windows. I have Windows 8.1 (legit copy) on my computer, but since this is a mid 2010 model MBP, it has quite a few "kinks" that I would LOVE to have resolved. Aside from that, I would like to have features such as Airplay mirroring that I do use/will use WAY more than she does.

Like I said, those are just a couple reasons, but certainly not all. If it was just a matter of cloning the hdd's, then I wouldn't be asking, but when it comes to BootCamp, that's a beast I'd rather not tackle again if I don't have to. it was hard enough just getting it on there (I had Win7 on there, then upgraded to Win8 then to Win8.1). Since all of the drivers don't work (yes, I have actually tried everything I know to do and was suggested to do) because my hardware is a bit older than hers, I figured if I could simply swap my hdd out in place of hers, I could have a working Windows 8.1 OS after I'm able to actually update/install the proper drivers.

Both are running Mavericks 10.9.2. Any assistance/info would be greatly appreciated.

Also, even though I have a legit copy of Win8.1, it was installed last semester in college, since I'm not in school this semester, I no longer have access to the website that I downloaded the OS from, so I can't simply backup my Windows, go through the BootCamp process again, then restore the backup because I can't redownload the OS.