How can I tell if there's a character waiting on a filehandle?

You should check out the Frequently Asked Questions list in comp.unix.* for things like this: the answer is essentially the same. It's very system dependent. Here's one solution that works on BSD systems: 

    sub key_ready {
	my($rin, $nfd);
	vec($rin, fileno(STDIN), 1) = 1;
	return $nfd = select($rin,undef,undef,0);
    }

You should look into getting the ReadKey extension on CPAN.