Not answering your more general question (which I don't understand), but note that you can easily generate a log file name with the current date/time in it with simple Perl. For example:

sub get_datestamp
{
   my ($s, $m, $h, $d, $mon, $y) = localtime;
   sprintf('%02d%02d%04d', $d, $mon + 1, $y + 1900);
}

my $logfile = 'filename_' . get_datestamp() . '.log';
print "logfile='$logfile'\n";
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This code works on any platform and has no need to interpolate bash command lines.