Probably should upgrade, FMP 11 was never tested on Yosemite for the very good reason that it did not exist at the time.
But FMP 13 files have a different format than 11 so your files on the old machine will not be compatible with the converted files on the new.
Roaringapps list compatibility, the ratings are sometimes limited to whether the apps starts up, not a guarantee that everything will work as expected.
I would test it and see. You can install FMP11 on both (but not run concurrently on a network). You may not have issues.
I highly recommend you download the 10.6.8 Combo update from Apple and install it.
Phil and David---Thanks so much for your prompt responses, information and suggestions.
And here's one more. If you haven't already purchased 13, you can download a free trial and use it to convert your current files as well as test them for issues. This is thus a no cost way to evaluate any issues you may have to deal with when you upgrade.