Regexp directives (like .) lose their special meaning inside character classes. You want
qr/^.{0,1000}$/s
or
qr/(?s:^.{0,1000}$)/

In character classes,

• A leading ^ will negate the character class.
• You can use Perl double-quote escapes (e.g. \x12, \cZ).
• $ and @ start variable interpolation (e.g. $var, @var, $var[4]).
• You can use Perl character classes (e.g. \d, \w, \s).
• You can use POSIX character classes (e.g. [:digit:], [:word:], [:space:])
• A dash can be used to create ranges (e.g. a-z).
• A slash (\) will cause the next character to be interpreted literally.
• Any other character (including ., * and +) will be matched literally.

Update: Added list.