Instead of

print $doc1->toString();
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you do

open XML, ">some.xml";
print XML $doc1->toString();
close XML;
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UPDATE: there is also a toFH function according to the documentation of XML::LibXML:

  # save
  open my $out, '>', 'out.xml';
  binmode $out; # as above
  $doc->toFH($out);
  # or
  print {$out} $doc->toString();
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