my %order;
@order{qw(Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec)} = (1..12);
...
my @sorted_filenames = sort {
  $order{substr($a,0,3)} <=> $order{substr($b,0,3)}
} @unsorted_filenames;
[download]

This'll be ok up to 100 filenames or so. If you have more, you'll probably want to cache the substr-naming mapping using a Schwartzian Transform or other device.

Or, you could even go for a merge sort, which will scale for 1000's of filenames:

my %piles;
for (@unsorted_filenames) {
  push @{$piles{substr($_, 0, 3)}), $_;
}
my @result;
for (qw(Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec)) {
  push @result, sort @{$piles{$_}};
  delete $piles{$_};
}
die if keys %piles; # unexpected prefix!
[download]

-- Randal L. Schwartz, Perl hacker