There should be no serious problems with transferring the hard drive.
The older MacBook Pro can't have as much RAM installed as you have now in your MacBook.
If I were doing that swap from one Mac to another, different model - I would boot to the Recovery partition, and reinstall Mavericks. That will assure that the various hardware drivers are detected as part of the OS X install, and installed properly (I think of that kind of reinstall as a "re-fit" )
That may not technically be necessary, but it's what I would do.