change database encoding without corrupting data (latin9 to utf8)

I have a problem to entry data to postgres database (latin9) from my
perl/tk application running on windows (utf8). Whenever I try to entry
letter with accents, these looks corrupted once stored into database.

A workaround is to set client encoding to UTF8 after creating the
database connection:

$dbh->do(qq/SET client_encoding to 'UTF8'/);

To avoid such kind of workaround I'd like to convert the whole
database from LATIN9 to UTF8, how can I do it without corrupting the
data?

Thanks,
Filippo