Looks to me like that should work as you want. Here's what I did to test it out:

#!/usr/bin/perl -w
# parent.pl
use strict;

if (my $pid = fork) {
  print "parent: child pid is $pid\n";
} else {
  exec('./child.pl');
}

#!/usr/bin/perl -w
# child.pl
use strict;

print "Child: pid is $$\n";
[download]

And the output I got was:

parent: child pid is 26534
Child: pid is 26534
[download]

--
<http://www.dave.org.uk>

"The first rule of Perl club is you don't talk about Perl club."