Here's one way to do this:

use strict;
use warnings;

my %hash_of_hashes=(
    'A'=>{'param'=>9, 'number'=>1},  
    'B'=>{'param'=>4, 'number'=>1}, 
    'C'=>{'param'=>5, 'number'=>1}, 
    'D'=>{'param'=>12, 'number'=>1},
);
for my $key (sort {$hash_of_hashes{$a}{param} <=> $hash_of_hashes{$b}{
+param}} keys %hash_of_hashes) {
  print "$key\n";
}
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You might also find the following useful:

• Perl data structures cookbook - hashes of hashes
• Resorting to Sorting
• Sort::Maker