I'd say that it's not a missing font, per se.
More likely either a system setting that has gone awry (the font choice), or perhaps a font cache file (try clearing your font caches, then restart). Another method to try for those font caches is to boot into Safe Mode - Restart, while holding the Shift key. You can release the shift when you see the rotating gear. You will get an account login window, even if your system is set for automatic logic. The Safe Boot mode will take considerably longer than normal - sometimes 10 minutes or so, which is completely normal. Some system cache cleanup can take place during that boot.
You didn't say what OS X version you have.
Another possible fix is to download and reinstall your current OS X combined updater. That can often help out with fixing a variety of odd system behaviour, and takes much less time than reinstalling everything.
Again, I don't know what OS X version you have, but here's the combined updater for a Snow Leopard (OS X 10.6.x) system:
http://support.apple.com/kb/DL1399
If you have another OS X version (10.5, 10.7, 10.8, etc) then just search at the Apple downloads for what you need. I can also give you a good link for another if you let me know which version you have now.
To answer your question about migration, I would doubt that a simple migration will cause the same issue on a different system. But, you probably should fix before you move on to another Mac, anyway.