the page isn't really ever refreshing so you don't need to re-request the data using LWP::Useragent. Just search through the response content for the var numHits line like: 
my $response = LWP::UserAgent->request($request);
my $total_hits = 0;
if($response->content =~ m/var numHits = '(\d+)'/){
    $total_hits = $1;
}

[download]
You can do something similar to get the numPages value but you shouldn't need to re-request the page.

In reply to Re^3: refreshing a page/session without re-submitting search by bpphillips
in thread refreshing a page/session without re-submitting search by seaver

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