Problems are always possible when you convert a file from one format to another. There have not been a large number of such reports posted in this forum but there have been a few.
But the original copy of the file is maintained unchanged when you do this. And you can download a free trial copy of Filemaker 13 and try converting your file to see if your specific file has any issues due to conversion without spending any dollars to find this out. And if you do encounter an issue, you are welcome to get assistance here in resolving the issue.
Here's a knowledgebase article as the file conversion process:
Converting to .fmp12 format: http://help.filemaker.com/app/answers/detail/a_id/10571/kw/converting
Thanks so much. I'm also considering upgrading from Mac 10.8.5 to Mavericks. I understand that FMP 11 is not supported on Mavericks, but FMP 13 is. Any major problems with (1) upgrading to Mavericks and (2) upgrading to FMP 13?