Because it's "what I do" ... here's the DateTime solution. I know you're already working in Time::Piece, so you probably want to go with the matching solution above.

use DateTime;

my $start_date = new DateTime( year => 2005, month => 10, day => 1  );
my $end_date   = new DateTime( year => 2005, month => 10, day => 14 );

while( $start_date <= $end_date ) {
   push( @{$result{ $start_date->day_name }}, $start_date->clone );
   $start_date->add( days => 1 );
}
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