Move my @doc inside the loop so you get a new instance of the doc array each time through. Consider:

use strict;
use warnings;

my @doc_nums = qw(1 2 3 4 5 6 7 8 9);
my @docs;

foreach( @doc_nums ) {
    my @doc;
    
    push @doc, int rand 10 for 1..3;
    push @docs, \@doc;
}

print "@$_\n" for @docs;
[download]

Prints:

9 5 8
9 5 7
2 2 1
3 0 4
8 6 4
6 1 7
6 5 5
8 6 9
9 9 7
[download]

or you could change the reference to a copy:

use strict;
use warnings;

my @doc_nums = qw(1 2 3 4 5 6 7 8 9);
my @docs;
    my @doc;

foreach( @doc_nums ) {
    @doc = ();
    push @doc, int rand 10 for 1..3;
    push @docs, [@doc];
}

print "@$_\n" for @docs;
[download]