Given that the dates are in one format but need to be sorted as if in another, you just need to control the behaviour of sort by inserting a sort block immediately after the sort keyword (see also
sort command syntax). In this case it is also a good idea to make a separate reformatting subroutine - the conversion to dd/mm/yyyy you carry out earlier might also be yet another formatting subroutine if you want your code to look more readable. (updated to show a simple way to get the last date)
my $lastdate;
foreach my $date
# n.b. $a and $b interpreted specially in a sort block
( sort { sFormat( $a ) <=> sFormat( $b ) }
keys %datecount
) {
print "\n", $date, ": ", $datecount{$date};
$lastdate = $date; # overwritten in order until last
}
sub sFormat { # convert dd/mm/yyyy into yyyymmdd
my $old = shift;
$old =~ /^(\d{2})\/(\d{2})\/(\d{4})$/
or die "Programming error: Invalid format $old\n";
return $3 . $2 . $1;
}