I can't think of any way to access object names to use as column labels.
You could set set up a staging table with the correct field names. You can import the records into this table, then do a merge file export to get a CSV file with a header row of field names.
But there may be better options than this...
You could do this using an external program using Java/JDBC against your FMP database, and even do the import into the other database directly all from the same code. Or you could just generate the CSV with the headings you want and then import manually into the other program.
But....since FMP doesn't, as I know, have an API where you can read the heading you want, you would need to have the headings in an external configuration file or, better yet, a table in FMP where you could read those too from the same JDBC logic. Not really sure all that work would be better than just straight FMP in this case, however.
FMP ships with a decent JDBC driver (unless you're working with container fields, where it's buggy). I've used it for lots of stuff and that code is not difficult.
HOPE THIS HELPS.