On unix you can use this piece of code to add a timestamp to every line written to the log file:

select STDOUT;
$| = 1;
unless (open STDOUT, "|-") {
    eval {
        while(<>) {
            my $now = DateTime->now;
            print "$now: $_";
        }
    };
    exit(0);
}
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It uses DateTime to generate the timestamp but changing it to use localtime should be pretty simple.