I'll just expand on this so that it sorts on the key that starts with "doc" and ends with a number. This removes the "there must be only one key" requirement.

my @sorted_aoh = sort {
    (map /^doc(\d+)/ ? 0+$1 : (), keys(%$a))[0]
    <=>
    (map /^doc(\d+)/ ? 0+$1 : (), keys(%$b))[0]
} @aoh;
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That happens to be suboptimal because every comparison is doing a potentially expensive operation to each hash. An improvement would be to use a Guttman-Rossler transform and then you get something really slick.

my @sorted_aoh =
map $aoh[ substr $_, 5 ],
sort
map {
    # Retrieve the document number
    my $doc_key = (map /^doc(\d+)$/ ? 0 + $1 : (), keys %{$aoh[$_]})[0
+];

    # Return the document number, a null and the original array index
    pack( 'N', $doc_key ) . "\0" . $_;
} 0 .. $#aoh
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