If you want to stay with Date::Manip, you'll have to feed the parser with a valid date: 'NOV-07' is not a date, but a month (there is no day specified).
Taking care of that, the following code works:
#!/usr/bin/perl
use strict;
use warnings;
use Date::Manip;
my $thingy = 'NOV-2007';
my $date = UnixDate( ParseDate( "1-$thingy" ), '%Y/%m' );
print "$date\n";