You didn't mention in what way(s) it's not working. That's important info for anyone trying to help you debug.

One issue I noticed is that you're going to run passed the end of @dude. The scalar value returned by @dude is the number of elements it contains. @dude+1 is one more than the number of elements.

Another issue is here: file"+"$0.txt ". Perl doesn't concatenate strings using '+'. It uses the dot operator for that. But it's not even necessary. You could write it as file$0.txt".

Here's a reworked version. I won't be debugging your system call, and don't know if it's even an issue:

use strict;
use warnings;

open FILE, '<', "dns.txt" or die $!;

while (my $line = <FILE>) {
  my ($ip) = $line =~ /(\d+\.\d+\.\d+\.\d+)/;
  system("ssh a.AS1 traceroute $ip > file$ip.txt");
}
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