Some options:

1. parent sends kill signal to child when parent processing is complete. Child dies. parent reaps child and exits (or continues, I suppose).
2. reverse the roll of parent and child. The child does the computing and the parent handles the counting&display. Child exits when complete and parent reaps child via SIG CHLD handler.

if(my $pid=fork){
  while(my $c = ReadKey){
     #doing something... ;
  }
  kill( HUP => $pid );
  wait(0);
}
else {
  my $count = 0;
  while(1){
     sleep(1);
     print $count++;
  }
}
[download]

if(my $pid=fork){
  #parent
  my $run = 1;
  $SIG{CHLD} = sub { 
    $deadchildpid = wait;
    $run = 0
  };
  my $count = 0;
  while($run){
     sleep(1);
     print $count++;
  }
}
else {
 #child
 while(my $c = ReadKey){
     #doing something... ;
  }
}
[download]