If you want to use the % operator, it can be quite simple. To expand on the GP anonymonk's script:

#!/usr/bin/env perl 
use strict;
use warnings;

# Set an array of names
my @names = qw/January February March April May June
    July August September October November December/;
# Find the index number of next month
my $next = (localtime)[4] + 1;

# Loop over the next 12 months and print the month names in sequence
for my $monpos ($next .. $next + 11) {
    print "Month is $names[$monpos % 12]\n";
}
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Please ask if anything in this piece of code is unclear.