Maybe not super efficient in terms of time, but at least terse:

for ([qw/dog good/],[qw/food fodder/]) {
   my ($first, $second) = @$_;
   print "$first does ";
   print "not "
      unless join("",sort split //,$second) =~ join(".*",sort split //
+,$first);
   print "contain $second\n";
}
[download]

I do this in word twist, which you may want to look at.

join("",sort split //,$first) =~ ("^".join("?",sort(split //,$second))
+."?\\z")
[download]

is possibly a faster way - I haven't benchmarked.