Did you want each row to be a different queue item?

while (my $row = $sth->fetch()) {
    # Must copy since fetch reuses array.
    $row = [ @$row ];

    $q->enqueue(share($row));
}
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You will be using threads right? Otherwise a queue is simply:

my @queue;

# Put stuff in
while (...) {
    push @queue, ...;
}

# Take stuff out
while (@queue) {
    my $item = shift(@queue);
    ...
}
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