Here's a basic solution using only core modules:
use Time::Local;
$date = '30Nov00';
my @months = qw/Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec/;
my $i = 0;
my %months = map { $_ => $i++ } @months;
my @dmy = $date =~ /(\d+)([A-Z]+)(\d+)/i;
$dmy[1] = $months{$dmy[1]};
if ($dmy[2] < 60) { # have to handle two-digit
$dmy[2] += 100; # year somehow
}
my $time = timelocal(0, 0, 12, @dmy); # noon, to avoid DST issues
$time += 60 * 60 * 24; # advance one day
my @dmy = (localtime($time))[3, 4, 5];
$dmy[1] = $months[$dmy[1]];
$dmy[2] %= 100;
my $date2 = sprintf "%02d%s%02d", @dmy;
print "$date2\n";
Of course, you could have Date::Parse and Date::Manip do most of the work for you, if you wanted.