• You have an off-by-one error for the months.
• The last line of your loop is a no-op.
• @date_array is redundant.
• A C-style for loop works great here.
• strftime is most appropriate here.
• 86400 is better written as 24*60*60. The latter is self-documenting.
• I prefer to use timegm/gmtime instead of setting the time to noon.

use strict;
use warnings;

use POSIX       qw( strftime );
use Time::Local qw( timegm );

my ($y1,$m1,$d1) = (2007,23,11);
my ($y2,$m2,$d2) = (2007, 4,12);

my $date1 = timegm(0,0,0,$d1,$m1-1,$y1);
my $date2 = timegm(0,0,0,$d2,$m2-1,$y2);

my @dates;
for (my $date=$date1; $date<=$date2; $date+=24*60*60) {
   push @dates, strftime('%Y-%m-%d', gmtime($date));
}
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