If you're doing a one-time transfer between two databases, it sounds to me like Perl might not be a great choice. What I would do is find out how to use the bulk loading facility in whatever your target database is. Then write a query to extract the data from the first database and save it to a file in the correct format for the second databases' bulk load program. Actually, for this purpose Perl might be a good choice. If you are writing a text file, a module like Text::Template or Text::CSV depending on how fancy it is.

If you do decide to go the straight Perl way, you should at a minimum use pleaceholders for the insertion step. Something like

my $sth_insert = $dbh2->prepare("insert into back_table_2 (abc1,abc2,a
+bc3)                  
                                   VALUES (?, ?, ?) ");
while ($row = $sth->fetchrow_arrayref) {
    $sth_insert->execute(@$row);
}
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and you might want to do a periodic commit as well.