My principles are:

• for plain lists use arrays (or array references),
• for lists with named attributes use hashes (or hash references).

So both on the router level and on the peer level you have plain lists, otherwise you have named attributes. So I would propose the following, which also allows for a simpler iteration over the structure:

use strict;
use warnings;

my $router_data = [ # array of hashes for each router
    { # hash for router 1
        routerName => 'asr01',
        ipAddr     => '1.1.1.1',
        bgpPeer    => [ # array of hashes for each peer
            { # hash for first peer
                Name       => 'PEER1',
                ASN        => '111',
                prefixList => 'PREFIX-PEER1-OUT',
            },
            { # hash for second peer
                Name       => 'PEER2',
                ASN        =>  '222',
                prefixList => 'PREFIX-PEER2-OUT',
            },
            ],
    },
    { # hash for router 2
        routerName => 'asr02',
        ipAddr     => '2.2.2.2',
        bgpPeer    => [ # array of hashes for each peer
            { # hash for first peer
                Name => 'PEER1',
                ASN  => '333',
                prefixList => 'PREFIX-PEER1-OUT',
            }
            ],
    },
    ];

for my $router ( @$router_data ) {
    print $router->{routerName}." : \n";
    for my $peer ( @{ $router->{bgpPeer} } ) {
        print $peer->{prefixList}."\n";
    }
}
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