Well, I was going to direct you to the Net::Ping module, but Net::Ping doesn't actually tell you how long the send/receive cycle took. So, I'd suggest calling ping via the shell and parsing its output:

my $output = grep {/round-trip/} `ping -c N foo.bar`;
my ($avg, $stddev) = ($output =~ m|([0-9.]+)/[0-9.]+/([0-9.]+) ms$|);
print "Average round-trip time: $avg (standard deviation $stddev)\n";
[download]

Or something like that... haven't tested this code.

I'm surprised that my cursory search of CPAN didn't turn up anything that'll do this for you.