I am keeping with you approach of sorting strings using lexicographic order and I am supposing that you know how to parse the dates. You need to use the format %02s in sprintf so that the first day of the week and the first month of the year are represented with 2 digits. You can use a subroutine like date2str below and sort the resulting strings.

sub date2str {
   my (  $month, $day, $year, $rest } = @_;
     sprintf( "%04d%02d%02d%s", $year, $month, $day, $rest );
}
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-- stefp