The diamond operator (readline) slurps all of the contents when used in list context. When using standard input, the termination is (under *nix) ^D - End Of Transfer.
You'll need to read in the items one by one:

print "...\n"
my @input;
while (<STDIN>) {
    last if /^q$/;
    push @input, $_;
}
print reverse @input;
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I used the regex ^q$ so the trailing newline is optional (not possible when using console input, but it is possible when piping: cat script | perl reverse.pl).

++ vs lbh qrpbqrq guvf hfvat n ge va Crey :)
Nabgure bar vs lbh qvq fb jvgubhg ernqvat n znahny svefg.
-- vs lbh hfrq OFQ pnrfne ;)
    - Whreq