You are very close. To query each nameserver once, put your nameservers in a list and iterate through the list, assigning each nameserver once to a resolver and querying it. See the following: 
use Net::DNS;
use strict;

my @nameservers=("192.168.1.1", "192.168.2.2", "192.168.3.3");
my $nameserver;
foreach $nameserver(@nameservers){
  print "checking on $nameserver\n";
  my $res = new Net::DNS::Resolver;
  $res->nameservers($nameserver);
  my $query = $res->search("www.perlmonks.com");
  if ($query) {
    my $rr;
    foreach $rr ($query->answer) {
      next unless $rr->type eq "A";
      print $rr->address, "\n";
    }
  }else {
    print "query failed: ", $res->errorstring, "\n";
  }
}

[download]
If you assign multiple nameservers to one resolver, it will use them as alternate nameservers in case it doesn't hear back from one of the others.

In reply to DNS Querying Multiple Resolvers in Series - Re: OO by lhoward
in thread OO, Net::DNS host lookup, multiple nameservers by ybiC

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.